Differential equation Definition and 1000 Threads

In mathematics, a differential equation is an equation that relates one or more functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly.
Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.

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  1. C

    Convolution Integral and Differential Equation

    I am really confused where to start with this problem. I know about convolutions somewhat. We have done them a little. Where is a good place to begin with this problem?
  2. K

    Need Help with Heterogeneous Differential Equation

    Hi Everyone! I am really stuck at one differential equation: (p-y)^{2}y'(x)+(x-y)(x+y-2p)=0 where p<x<1; \ 0<y<p; \ p - parameter, 0<p<1 I have a suspicion that it does not have a solution, but is there a way to prove it mathematically in this case? I would appreciate any hints on...
  3. djh101

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    Homework problem for nonlinear dynamics. Let us write xλ(t) for the solution of the initial value problem \dot{x} = f(x) & x(0) = λ where f is continuously differentiable on the whole line and f(0) = 0. a) Find the differential equation for \frac{∂x_{λ}}{∂λ}(t) I'm a little confused...
  4. M

    Differential Equation with unit step function and Laplace transforms

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  5. D

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  6. N

    Finding the equilibrium points of a differential equation

  7. P

    Solution to Bessel's Differential Equation

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  8. N

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  9. N

    Seperable Differential equation

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  10. D

    Why Am I Getting a Complex Answer for the Current Through the Resistor?

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  11. D

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  12. W

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  13. P

    MATLAB Differential Equation formulation (and execution in matlab) problem

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  14. S

    Four differential equation problems

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  15. M

    Question regarding Bernoulli Differential Equation

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  16. M

    How does one get the solution to the differential equation for SHM?

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  17. E

    Solution of this differential equation

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  18. A

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  19. Logan Land

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  20. Logan Land

    MHB Solving a linear first order differential equation

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  21. J

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  22. D

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  23. marellasunny

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  24. F

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  25. S

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  26. A

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  27. A

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  28. J

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  29. M

    Need help solving this differential equation

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  30. G

    Differential equation d^2f/dx^2-(3-2i)f=0

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  31. H

    Minimum value of n for non-zero 4th derivative in Euler-Bernoulli beam equation

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  32. r-soy

    MHB Solving an Exact Differential Equation (#2)

  33. r-soy

    MHB Solving an Exact Differential Equation (#1)

  34. A

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  35. B

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  36. M

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  37. I like Serena

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  38. S

    Ordinary Differential Equation

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  39. J

    How Can I Solve This Differential Equation for Y?

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  40. J

    Can this differential equation be solved analytically or numerically?

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  41. S

    MHB Simultaneous differential equation

    Solve: dx/dt +2y+ex=t2 dy/dt-x+xex=0 Please help for this simultaneous differential equations
  42. Z

    Is this a differential equation and what do I need to be able to

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  43. M

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  44. A

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  45. Fernando Revilla

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  46. S

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  47. R

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  48. S

    Homogenous Ordinary Differential Equation

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  49. N

    (Differential equation) Finding an exponential equation

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  50. S

    Second Order Differential Equation (homogenous)

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