differential eqautions

  1. 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...
  2. 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...
  3. R

    Differential equation

    1. Homework Statement 2. Homework Equations euler ##e^{ix} = cos(x) + i*sin(x)## ##e^{-ix} = cos(x) - i*sin(x)## 3. 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...
  4. JD_PM

    Proving that a vector field is conservative

    1. Homework Statement 2. Homework Equations $$F = \nabla \phi$$ 3. The Attempt at a Solution Let's focus on determining why this vector field is conservative. The answer is the following: I get everything till it starts playing with the constant of integration once the...
  5. 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 $A=V_0^2/(8RhL)$...
  6. Z

    Differential Equation with an Initial condition

    1. Homework Statement x(dy/dx) = 3y +x4cos(x), y(2pi)=0 2. Homework Equations N/A 3. 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...
  7. 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##: $$ \frac{\sigma_I}{r} \frac{\partial}{\partial r} \left(r \frac{\partial z(r,t)}{\partial r} \right)=\rho_D gz(r,t)-p(r,t)-4 \mu_T \frac{\partial^2z(r,t)}{\partial r^2} \frac{\partial z(r,t)}{\partial t} $$...
  8. 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...
  9. W

    Finding Orthogonal Trajectories (differential equations)

    1. 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## 2. Homework Equations 3. The Attempt at a Solution substituting ##x## and ##y## I get...
  10. Jozefina Gramatikova

    Separate the following PDE as much as possible

    1. Homework Statement 2. Homework Equations 3. The Attempt at a Solution Could you tell me is there something specific that I need to the with sin(xy)? Thanks
  11. P

    I Rewriting ODEs

    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}-...
  12. A

    I Linearity of DE's

    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?
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. Differential Equations and Applications (NPTEL):- Lecture 15: Well-posedness and Examples of IVP

    Differential Equations and Applications (NPTEL):- Lecture 15: Well-posedness and Examples of IVP

    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
  28. Differential Equations and Applications (NPTEL):- Lecture 16: Gronwall's Lemma

    Differential Equations and Applications (NPTEL):- Lecture 16: Gronwall's Lemma

    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
  29. Differential Equations and Applications (NPTEL):- Lecture 17: Basic Lemma and Uniqueness Theorem

    Differential Equations and Applications (NPTEL):- Lecture 17: Basic Lemma and Uniqueness Theorem

    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
  30. Differential Equations and Applications (NPTEL):- Lecture 18: Picard's Existence and Uniqueness Theorem 1

    Differential Equations and Applications (NPTEL):- Lecture 18: Picard's Existence and Uniqueness Theorem 1

    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
Top