What is Differential eqautions: Definition and 94 Discussions

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  1. 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
  2. Differential Equations and Applications (NPTEL):- Lecture 19: Picard's Existence and Uniqueness Theorem 2

    Differential Equations and Applications (NPTEL):- Lecture 19: Picard's Existence and Uniqueness Theorem 2

    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
  3. Differential Equations and Applications (NPTEL):- Lecture 20: Cauchy Peano Existence Theorem

    Differential Equations and Applications (NPTEL):- Lecture 20: Cauchy Peano Existence 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
  4. Differential Equations and Applications (NPTEL):- Lecture 21: Existence using Fixed Point Theorem

    Differential Equations and Applications (NPTEL):- Lecture 21: Existence using Fixed Point 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
  5. Differential Equations and Applications (NPTEL):- Lecture 22: Continuation of Solutions

    Differential Equations and Applications (NPTEL):- Lecture 22: Continuation of Solutions

    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
  6. Differential Equations and Applications (NPTEL):- Lecture 23: Series Solution

    Differential Equations and Applications (NPTEL):- Lecture 23: Series Solution

    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
  7. Differential Equations and Applications (NPTEL):- Lecture 24: General System and Diagonalizability

    Differential Equations and Applications (NPTEL):- Lecture 24: General System and Diagonalizability

    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
  8. Differential Equations and Applications (NPTEL):- Lecture 25: 2 by 2 systems and Phase Plane Analysis 1

    Differential Equations and Applications (NPTEL):- Lecture 25: 2 by 2 systems and Phase Plane Analysis 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
  9. Differential Equations and Applications (NPTEL):- Lecture 26: 2 by 2 systems and Phase Plane Analysis 2

    Differential Equations and Applications (NPTEL):- Lecture 26: 2 by 2 systems and Phase Plane Analysis 2

    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
  10. Differential Equations and Applications (NPTEL):- Lecture 27: General Systems

    Differential Equations and Applications (NPTEL):- Lecture 27: General Systems

    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
  11. Differential Equations and Applications (NPTEL):- Lecture 28: General Systems Continued and Non-homogeneous Systems

    Differential Equations and Applications (NPTEL):- Lecture 28: General Systems Continued and Non-homogeneous Systems

    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
  12. Differential Equations and Applications (NPTEL):- Lecture 29: Basic Definitions and Examples

    Differential Equations and Applications (NPTEL):- Lecture 29: Basic Definitions and Examples

    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
  13. Differential Equations and Applications (NPTEL):- Lecture 30: Stability Equilibrium Points 1

    Differential Equations and Applications (NPTEL):- Lecture 30: Stability Equilibrium Points 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
  14. Differential Equations and Applications (NPTEL):- Lecture 31: Stability Equilibrium Points 2

    Differential Equations and Applications (NPTEL):- Lecture 31: Stability Equilibrium Points 2

    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 32: Stability Equilibrium Points 3

    Differential Equations and Applications (NPTEL):- Lecture 32: Stability Equilibrium Points 3

    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 33: Second Order Linear Equations 4

    Differential Equations and Applications (NPTEL):- Lecture 33: Second Order Linear Equations 4

    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 34: Lyapunov Function 1

    Differential Equations and Applications (NPTEL):- Lecture 34: Lyapunov Function 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
  18. Differential Equations and Applications (NPTEL):- Lecture 35: Lyapunov Function 2

    Differential Equations and Applications (NPTEL):- Lecture 35: Lyapunov Function 2

    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 36: Periodic Orbits and Poincare Bendixon Theory 1

    Differential Equations and Applications (NPTEL):- Lecture 36: Periodic Orbits and Poincare Bendixon Theory 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
  20. Differential Equations and Applications (NPTEL):- Lecture 37: Periodic Orbits and Poincare Bendixon Theory 2

    Differential Equations and Applications (NPTEL):- Lecture 37: Periodic Orbits and Poincare Bendixon Theory 2

    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 38: Linear Second Order Equations

    Differential Equations and Applications (NPTEL):- Lecture 38: Linear Second Order 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
  22. Differential Equations and Applications (NPTEL):- Lecture 39: General Second Order Equations 1

    Differential Equations and Applications (NPTEL):- Lecture 39: General Second Order Equations 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
  23. Ordinary Differential Equations and Applications (NPTEL):- Lecture 40: General Second Order Equations 2

    Ordinary Differential Equations and Applications (NPTEL):- Lecture 40: General Second Order Equations 2

    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. phantom lancer

    Method of undetermined coefficients -- Help please

    Homework Statement Using the method of undetermined coefficients, determine the general solution of the following second-order, linear, non-homogenous equations. y'' - 4y' + 4y = 2e^(2x+3) Homework Equations I'm not sure what to do from here... Also, I'm new here. How do I use the superscript...
  25. A

    I How to find a solution to this linear ODE?

    I want to find solution to following ODE $$ \frac{d \bar h}{dt} + \frac{K}{S_s} \alpha^2 \bar h = -\frac{K}{S_s} \alpha H h_b(t) $$ I have solved it with integrating factor method with ## I=\exp^{\int \frac{1}{D} \alpha^2 dt} ## as integrating factor and ##\frac{K}{S_s} = \frac{1}{D} ## I have...
  26. J6204

    Determing the differences between two sets of differential eqs

    Homework Statement Given the following figure and the following variables and parameters, I have been able to come up with the set of differential equation below the image. My question is how does the system of equations 1 which I produced myself differ from the set of equations 2. Below I have...
  27. 6

    Find the path of a particle given a potential function.

    I am tasked with finding the path a particle takes through this potential field. $$U(x,y) = x^2+xy+y^2$$ I then took the gradient, and this produced a pair of differential equations. $$\frac{d^2x}{dt^2}=\frac{1}{m}(-2x-y)$$ $$\frac{d^2x}{dt^2}=\frac{1}{m}(-2y-x)$$ I have yet to encounter set of...
  28. V

    2D equation for projectile with linear drag force

    Homework Statement Given the equations a) find the solution to the problem (1) in vectorial form, by first writing equation (1) in component form and then solving the two parts separately. These can then be combined to obtain the vector form of the solution. b) solve the results of the...
  29. I

    A A system of DEs with variable coefficients.

    Hi. I have been trying for sometime to solve the following system of DEs analytically(Is it possible?) but no luck so far. $$x''(t)=-z(t)x'(t)-x(t)+y(t),$$ $$y'(t)=-z(t)y(t)+x^2(t)$$ $$z'(t)=-2z^2(t)-x(t)$$. With the initial conditions ##x(0)=1## , ##x'(0)=0## ,##y(0)=0## and ##z(0)=1##...
  30. W

    Mathematica Rescaling equations in Mathematica

    Suppose I have a differential equation $$\ddot \phi + 3H (1+Q) \dot \phi + V_{,\phi} = 0$$ where ##\phi## is the inflaton field. ##H## is the Hubble parameter, ##Q## is just a number, ##V_{,\phi}## is the derivative with respect to ##\phi##, and initial conditions given by ##\phi[0] = 2...
  31. Boosh

    Hydrogen radial equation solution

    I am going through my Quantum textbook, just reviewing the material, i.e. this isn't a homework question. We are solving the radial equation for the Hydrogen Atom, first looking at the asymptotic behavior. My issue is I am completely blanking on how to solve the differential equation...
  32. dumbdumNotSmart

    Critically Damped System - Viscous force

    Homework Statement You got a plate hanging from a spring (hookes law: k) with a viscous force acting on it, -bv. If we place a mass on the plate, gravity will cause it to oscillate. Prove that if we want the plate to oscillate as little as possible (Crticial damping, no?), then $$b=2m...
  33. gelfand

    Drag force with differential equations, finding max speed

    Homework Statement A submarine engine provides maximum constant force ##F## to propel it through the water. Assume that the magnitude of the resistive drag force of the water experienced by the submarine is ##kv##, where ##k## is the drag coefficient and ##v## is the instantaneous speed of...
  34. Poetria

    Damping and resonance

    Homework Statement x''+b*x'+k*x=k*y+b*y' y=cos(omega*t) k is fixed, b - damping constant slowly increases. How does increasing the damping constant b affect the resonance peak? 2. The attempt at a solution Well, I thought the answers: It significantly decreases the height of the...
  35. P

    I Similarities / diffs between diffusion & wave propagation

    Hi, I'm a second year undergrad and we've covered the heat equation, \begin{equation} ∇^{2}\Psi = \frac{1}{c^{2}}\frac{\partial^2 \Psi}{\partial t^2} \end{equation} and the wave equation, \begin{equation} D∇^{2}u= \frac{\partial u}{\partial t} \end{equation} in our differential equations...
  36. L

    Derivation of Rocket Equation Using Relative Velocity

    Based on my current understanding of the problem I do not see this following derivation as valid, although this is what was given in my course notes. Although this particular example is from an undergraduate physics course this is not a homework problem: I'm confused about the underlying...
  37. cheapstrike

    Doubt related to formation of a differential equation

    Homework Statement Find the order of the differential equation of y=C1sin2x+C2cos2x+C3. Homework Equations - The Attempt at a Solution [/B] I read in my book that the order of the differential equation is equal to the number of arbitrary constants but the answer given is 2. Btw I have...
  38. P

    Angular Frequency of a Piston with Ideal Gas

    Homework Statement A frictionless piston of mass m is a precise fit in the vertical cylindrical neck of a large container of volume V. The container is filled with an ideal gas and there is a vacuum above the piston. The cross-sectional area of the neck is A. Assuming that the pressure and...
  39. J

    Can somebody help me understand this BVP question?

    Homework Statement So I don't really understand what the professor means by "show why the displacements y(x,t) should satisfy this boundary value problem" in problem 1. Doesn't that basically boil down to deriving the wave equation? At least in problem 2 he says what he wants us to show...
  40. S

    I Hubble term versus inflaton

    From cosmology, ##H^2 = \frac{ρ}{3M_p^2} = \frac{1}{3M_p^2}(½\dot φ^2 + ½m^2φ^2)## Suppose ##V(φ) = ½m^2φ^2## where ##ρ## = density ##M_p## = Planck mass I want to graph ##H## vs. ##φ## but there is a ##\dot φ## and I know this is a differential equation, can somebody help me what to do here?
  41. C

    I Solution of an ODE in series Frobenius method

    Hi I am supposed to find solution of $$xy''+y'+xy=0$$ but i am left with reversing this equation. i am studying solution of a differential equation by series now and I cannot reverse a series in the form of: $$ J(x)=1-\frac{1}{x^2} +\frac{3x^4}{32} - \frac{5x^6}{576} ...$$ $$...
  42. G

    Finding maximum height of a string before it goes slack

    Homework Statement A mass m is suspended by a light elastic string. When the mass remains at rest it is at a point 0, which is a distance a + b below the point from which the string is suspended from the ceiling, where a is the natural length of the string. The mass is pulled down a distance h...
  43. Tspirit

    I How to solve the two following differential equations?

    (1) ##\frac{d^{2}y}{dx^{2}}=0## (2) ##\frac{d^{2}y}{dx^{2}}=k^{2}y##, where k is a real positive number.
  44. Elvis 123456789

    Lagrangian of two mass and spring/pulley system

    Homework Statement Two blocks of equal mass, m, are connected by a light string that passes over a massless pulley. One block hangs below the pulley, while the other sits on a frictionless horizontal table and is attached to a spring of constant k. Let x=0 be the equilibrium position of the...
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