Differential eqautions Definition and 96 Threads

  1. sergiokapone

    I Integral and differential forms of field equations

    I have a question, is there some other fundamental difference in the integral and differential form of the field equations that is missed here and should have been mentioned?
    • sergiokapone
    • Thread
    • Differential eqautions field equations Integral calculus Maxwel's equations
    • Replies: 16
    • Forum: Electromagnetism
  2. PLAGUE

    Books on D Operator Method

    TL;DR Summary: Comprehensive books on D Operator method Currently I am studying (Ordinary) Differential equation but the book I am following doesn't include much on D Operator Method of solving differential equations. Please suggest me some (Ordinary Differential Equation) books that goes...
  3. ematt

    A Symplectic split of Hamiltonian with complex term

    Is it possible to express symplectic split integrator for Hamiltonian containing an extra imaginary term? For instance H=T+V+iV_2
  4. Hamiltonian

    How Do You Solve a Differential Equation Using an Ansatz?

    Finding the first and second derivative of out ansatz, $$\dot x(t)=A(cos(\omega_0 t) - t\omega_0 sin(\omega_0 t)) + B(sin(\omega_0 t) + t\omega_0 cos(\omega_0 t))$$ $$\ddot x= A(-2\omega_0 sin(\omega_0 t) - t{\omega_0}^2cos(\omega_0 t)) + B(2\omega_0 cos(\omega_0 cos(\omega_0 t)...
  5. S

    B Why doesn't the Navier-Stokes equation have a solution?

    Why the navier-stokes equation don't have a solution ?
    • Sawawdeh
    • Thread
    • Differential eqautions Hydrodynamics
    • Replies: 5
    • Forum: Mechanics
  6. Lotto

    Movement of the water level in the barrel - calculate its velocity, etc.

    Here is only my solution: ##A_1 \frac{\mathrm d h}{\mathrm d t}=-A_2\sqrt{2hg}##, so by integrating we get ##h(t)=\left(\sqrt{h_0}-\frac{A_2}{2A_1}\sqrt{2g} t\right)^2.## Setting ##h(T)=0## we get ##T=\frac{A_1}{A_2}\sqrt{\frac{2h_0}{g}}.## By doing the first time derivative of ##h## we...
  7. P

    Relativistic particle moving in a potential

    Since energy is conserved and the particle is initially at rest, we can determine that ##E(0) = m_0 c^2##, so $$ m_0 c^2 = \sqrt{ c^2 p^2 + m_0^2 c^4 } + \alpha x. $$ Squaring this eqation gives $$ m_0^2 c^4 = \alpha^2 x^2 + c^2 p^2 + m_0^2 c^4 + 2 \alpha x \sqrt{ c^2 p^2 + m_0^2 c^4 }...
  8. H

    Mathematica How to check a particular solution of System of Linear ODEs?

    If I have been given a system of inhomogeneous linear ODEs, $$ \vec{x'} = \begin{bmatrix} 4 & -1 \\ 5 & -2 \\ \end{bmatrix} \vec{x} + \begin{bmatrix} 18e^{2t} \\ 30e^{2t}\\ \end{bmatrix} $$ I have found its particular solution to be: $$ 1/4 \begin{bmatrix} -31e^{2t} - 25e^{6t} \\ 85e^{2t} -...
  9. H

    Solving ##y'' - 5 y' - 6y = e^{3x}## using Laplace Transform

    We have to solve $$ \begin{align*} y'' - 5y' - 6y = e^{3x} \\ y(0) = 2,~~ y'(0) = 1 \\ \end{align*} $$ Applying Laplace Transform the equation $$ \begin{align*} L [ y''] - 5 L[y'] - 6 L[y] = L [ e^{3x} ] \\ s^2 Y(s) - \left( s y(0) + y'(0) \right) - 5s Y(s) + y(0) - 6 Y(s) = \frac{1}{s-3} \\...
  10. hagopbul

    I Drawing Direction Fields for Higher Order ODEs

    Hello : Trying to find references on drawing direction fields of higher order differential equation by hand as 1st step then by computer , do you know any reference I can read ( PDF , books ,...) , and hope it is not only some short notes Best regards HB
  11. J

    Using the Frobenius method on a 2D Laplace

  12. L

    Prove eigenvalues of the derivatives of Legendre polynomials >= 0

    The problem has a hint about finding a relationship between ##\int_{-1}^1 (P^{(k+1)}(x))^2 f(x) dx## and ##\int_{-1}^1 (P^{(k)}(x))^2 g(x) dx## for suitable ##f, g##. It looks they're the weighting functions in the Sturm-Liouville theory and we may be able to make use of Parseval's identity...
  13. Ibidy

    Struggling to find solution to 1D wave equation in the following form:

  14. potatocake

    Is My Solution to This Exact Differential Equation Correct?

    (x cos(y) + x2 +y ) dx = - (x + y2 - (x2)/2 sin y ) dy I integrated both sides 1/2x2cos(y) + 1/3 x3+xy = -xy - 1/3y3+x2cos(y) Then I get x3 + 6xy + y3 = 0 Am I doing the calculations correctly? Do I need to solve it in another way?
  15. D

    Prerequisite mathematics for intermediate mechanics?

    I will be taking intermediate mechanics next semester, and am a bit concerned about potential gaps in my mathematical knowledge. Long story short, I used to be a physics major, switched to electrical engineering, and then decided to double major after a semester in EE. The issue is that, as a...
    • dpatnd
    • Thread
    • Differential eqautions Linear algagbra Math and physics Mathematics Mechanics Prerequisites
    • Replies: 4
    • Forum: Mechanics
  16. quantumCircuit

    Lotka Volterra estimate parameters from experimental data

    Namely, in the system, I have obtained the value of parameters L, M, A and D, because I treat the other organism as equal to zero, i.e., it doesn't exist, but I am struggling about the values of B and C, that are coupled with the product of x and y. Can anyone help me how to obtain those values...
  17. M

    A Solving a differential equation with two unknowns

    One thing that is given in paper (attached) is a operating set point for temperature which is given as 20 for day and 16 for night but I do not know whether its initial condition for temperature or not. Can anyone please guide me that what kind of equation is it and how can I solve it with these...
  18. O

    I The Trapping Region of the Lorenz equations

    I was dealing with nonlinear systems of differential equations like the Lorenz equations (https://en.wikipedia.org/wiki/Lorenz_system). Now there is a trapping region of this system defined by the ellipsoid ρx^2+σy^2+σ(z-2ρ)^2<R. I wondered how this region is found and I found out that a...
  19. J

    Calculus What is the best textbook for understanding differentials?

    Hi, I am an undergrad looking to purchase a good textbook on differentials for my course which I will be taking soon, and the textbook listed for the differentials course is this one (https://www.amazon.com/gp/product/1118531779/?tag=pfamazon01-20) which apparently is not very good. So can...
  20. The Coronavirus Curve Simulation - Numberphile

    The Coronavirus Curve Simulation - Numberphile

    Ben Sparks uses https://www.GeoGebra.org to explain (and code) the so-called SIR Model being used to predict the spread of cornavirus (COVID-19). A pretty cool way to visualize a set of differential equations.
    • scottdave
    • Media item
    • Coronavirus Differential eqautions Numerical analysis
    • Comments: 1
    • Category: Differential Equations
  21. O

    How to prove this statement about the derivative of a function

    My try: ##\begin{align} \dfrac{d {r^2}}{d r} \dfrac{\partial r}{\partial p} = \dfrac{\partial {r^2}}{\partial p} \tag1\\ \dfrac{\partial r}{\partial p} = \dfrac{\partial {r^2}}{\partial p} \dfrac{1}{\dfrac{d r^2}{d r}}=\dfrac{p-a\cos\theta}{r} \tag2\\ \end{align}## By chain rule...
  22. J

    The range for y if t>=10 is [-4, 0].

    From integration by parts, and using y(10) = 0, I get the equation ##2e^{3t-30} = \frac{|y-2|}{|y+1|}.## Let ##f(t) = 2e^{3t-30}##. Since it's for t>10, f(10) = 2, and we have ##2=\frac{|y-2|}{|y+1|}##. Depending on the sign I choose to use, I get either that y=-4 or y =0. Since ##t: 10...
  23. A

    I When and How to Solve ODEs: Clarity for Confused Students

    I know how to solve ODEs using both methods. The problem I'm having is knowing when to use one and not the other. If someone could help clarify this for me. I can't find the correct section in my textbook.
  24. K

    Differential equation problem: Modeling the spread of a rumor on campus

    So this is what I have done: ##f'(t)=k*f(t)*(A-f(t))*(1-sin(\frac{pi*x}{12}))## ##\frac{1}{f(t)*(A-f(t))}=k*(1-sin(\frac{pi*x}{12}))## I see that the left can be written as this (using partial fractions): ##1/A(\frac{1}{f(t)}-\frac{1}{A-f(t)})## And then I take the integral on both sides and...
  25. aligator11

    Particle Dynamics Problem (kinematics)

    Summary: Mechanics problem related with Calculus (differential equations) Hi everyone, I would like some help in that task, if anyone would be willing to help :) Namely I have a problem from particle dynamics. "D:" means given info... so, D: m,g,h,b, miu. We're looking for v0 and S as given...
  26. christang_1023

    Solve the differential equation of motional emf

    . Above is the figure of the problem. I am trying to solve x(t) and differentiate it to obtain v(t); however, I have difficulty solving the differential equation shown below. $$ v(t)=\int a(t)dt=\int \frac{B(\varepsilon-Blv)d}{Rm}dt \Rightarrow \frac{dx}{dt}=\frac{B\varepsilon...
  27. R

    How do you solve a differential equation with complex numbers?

    Homework Statement Homework Equations euler ##e^{ix} = cos(x) + i*sin(x)## ##e^{-ix} = cos(x) - i*sin(x)## The Attempt at a Solution I'm starting with differential equations and I'm trying to understand this solution including complex numbers: First we determine the zeros. I understand that...
  28. JD_PM

    Proving that a vector field is conservative

    Homework Statement Homework Equations $$F = \nabla \phi$$ The Attempt at a Solution Let's focus on determining why this vector field is conservative. The answer is the following: [/B] I get everything till it starts playing with the constant of integration once the straightforward...
  29. B

    I Solution of the 1D heat equation

    $$\frac{\partial T}{\partial t}=\alpha\frac{\partial^2 T}{\partial^2 t}$$ with an initial condition and boundary conditions $$T(x,0)=T_0$$ $$T(L,t)=T_0$$ $$-k\left.\frac{\partial T}{\partial x}\right|_{x=0}=2A\cos^2\left(\frac{\omega t}{2}\right)=A(\cos\omega t+1)$$ where $A=V_0^2/(8RhL)$...
    • Betsy
    • Thread
    • 1d Differential eqautions Heat Heat and mass transfer Heat capacity Heat equation Thermal conductivity
    • Replies: 8
    • Forum: Differential Equations
  30. Z

    Differential Equation with an Initial condition

    Homework Statement x(dy/dx) = 3y +x4cos(x), y(2pi)=0 Homework Equations N/A The Attempt at a Solution I've tried a couple different ways to make this separable, but you always carry over a 1/dx or 1/dy term and I can never fully separate this. I've also tried to do a Bernoulli differential...
  31. T

    A Determine PDE Boundary Condition via Analytical solution

    I am trying to determine an outer boundary condition for the following PDE at ##r=r_m##: $$ \frac{\sigma_I}{r} \frac{\partial}{\partial r} \left(r \frac{\partial z(r,t)}{\partial r} \right)=\rho_D gz(r,t)-p(r,t)-4 \mu_T \frac{\partial^2z(r,t)}{\partial r^2} \frac{\partial z(r,t)}{\partial t} $$...
    • tse8682
    • Thread
    • Analytical Analytical solution Bessel function Boundary Boundary condition Condition Differential eqautions Ordinary differential equation Partial differential equations Pde
    • Replies: 1
    • Forum: Differential Equations
  32. thoraxepi

    I Transfer Function relating momentum and force

    Hey all, I hope this is the correct forum section to post this in. I heard about this problem from a youtube video but I've not been able to simulate it because the video was meant only for an introduction into PID control. Here's the problem: A remote control helicopter is hovering just...
    • thoraxepi
    • Thread
    • Differential eqautions Force Function Laplace transform Momentum Process control Transfer fucntion Transfer function
    • Replies: 2
    • Forum: Differential Equations
  33. W

    Finding Orthogonal Trajectories (differential equations)

    Homework Statement Find Orthogonal Trajectories of ##\frac{x^2}{a}-\frac{y^2}{a-1}=1## Hint Substitute a new independent variable w ##x^2=w## and an new dependent variable z ##y^2=z## Homework EquationsThe Attempt at a Solution substituting ##x## and ##y## I get...
  34. Jozefina Gramatikova

    Separate the following PDE as much as possible

    Homework Statement [/B]Homework Equations [/B]The Attempt at a Solution [/B] Could you tell me is there something specific that I need to the with sin(xy)? Thanks
  35. P

    I How does the substitution x = 1/z transform Bessel's Equation?

    Hi! When we want to look at different singular points for e.g Bessel's eq. $$u´´(x) + \frac{u'(x)}{x} + (1- \frac{n^2}{x^2})u(x)$$. We usually evaluate the equation letting x= 1/z. But I don't algebraically see how such a substitution ends up with $$w´´(z) +( \frac{2}{z}-...
  36. A

    I Understanding Linearity of Differential Equations

    Hey all, I don't understand what makes a differential equation (DE) linear. I found this: "x y' = 1 is non-linear because y' is not multiplied by a constant" but then also this: "x' + (t^2)x = 0 is linear in x". t^2 also isn't a constant. So why is this equation linear?
  37. Differential Equations and Applications (NPTEL):- Lecture 01: General Introduction

    Differential Equations and Applications (NPTEL):- Lecture 01: General Introduction

    COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED. Lectures: http://www.nptel.ac.in/courses/111108081/ Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
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  38. Differential Equations and Applications (NPTEL):- Lecture 02: Examples I

    Differential Equations and Applications (NPTEL):- Lecture 02: Examples I

    COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED. Lectures: http://www.nptel.ac.in/courses/111108081/ Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
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  39. Differential Equations and Applications (NPTEL):- Lecture 03: Examples II

    Differential Equations and Applications (NPTEL):- Lecture 03: Examples II

    COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED. Lectures: http://www.nptel.ac.in/courses/111108081/ Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
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  40. Differential Equations and Applications (NPTEL):- Lecture 04: Examples III

    Differential Equations and Applications (NPTEL):- Lecture 04: Examples III

    COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED. Lectures: http://www.nptel.ac.in/courses/111108081/ Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
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  41. Differential Equations and Applications (NPTEL):- Lecture 05: Linear Algebra I

    Differential Equations and Applications (NPTEL):- Lecture 05: Linear Algebra I

    COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED. Lectures: http://www.nptel.ac.in/courses/111108081/ Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
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  42. Differential Equations and Applications (NPTEL):- Lecture 06: Linear Algebra II

    Differential Equations and Applications (NPTEL):- Lecture 06: Linear Algebra II

    COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED. Lectures: http://www.nptel.ac.in/courses/111108081/ Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
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  43. Differential Equations and Applications (NPTEL):- Lecture 07: Linear Algebra III

    Differential Equations and Applications (NPTEL):- Lecture 07: Linear Algebra III

    COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED. Lectures: http://www.nptel.ac.in/courses/111108081/ Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
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  44. Differential Equations and Applications (NPTEL):- Lecture 08: Analysis I

    Differential Equations and Applications (NPTEL):- Lecture 08: Analysis I

    COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED. Lectures: http://www.nptel.ac.in/courses/111108081/ Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
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  45. Differential Equations and Applications (NPTEL):- Lecture 09: Analysis II

    Differential Equations and Applications (NPTEL):- Lecture 09: Analysis II

    COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED. Lectures: http://www.nptel.ac.in/courses/111108081/ Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
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  46. Differential Equations and Applications (NPTEL):- Lecture 10: First Order Linear Equations

    Differential Equations and Applications (NPTEL):- Lecture 10: First Order Linear Equations

    COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED. Lectures: http://www.nptel.ac.in/courses/111108081/ Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
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  47. Differential Equations and Applications (NPTEL):- Lecture 11: Exact Equations

    Differential Equations and Applications (NPTEL):- Lecture 11: Exact Equations

    COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED. Lectures: http://www.nptel.ac.in/courses/111108081/ Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
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  48. Differential Equations and Applications (NPTEL):- Lecture 12: Second Order Linear Equations I

    Differential Equations and Applications (NPTEL):- Lecture 12: Second Order Linear Equations I

    COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED. Lectures: http://www.nptel.ac.in/courses/111108081/ Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
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  49. Differential Equations and Applications (NPTEL):- Lecture 13: Second Order Linear Equations II

    Differential Equations and Applications (NPTEL):- Lecture 13: Second Order Linear Equations II

    COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED. Lectures: http://www.nptel.ac.in/courses/111108081/ Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
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  50. Differential Equations and Applications (NPTEL):- Lecture 14: Second Order Linear Equations III

    Differential Equations and Applications (NPTEL):- Lecture 14: Second Order Linear Equations III

    COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED. Lectures: http://www.nptel.ac.in/courses/111108081/ Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
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