Differential equations Definition and 999 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. B

    Modeling a car slowing down from speed

    Hello! I'm trying to model a car slowing down from speed with the forces of drag and friction and gravity from the road slope.. The model, which models the resistive forces is as follows.. [ Ffriction + Fdrag + Fslope ] / m = -a (deceleration) where: Friction force Ffriction = A...
  2. A

    MHB Determine dynamics of stochastic differential equations (SDE)

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  3. H

    Series Solution of Differential equations

    Working through Mathematical Methods in the Physical Sciences by Boas, on the chapter on Series Solutions of Differential Equations, Boas works the example: y' = 2xy Boas differentiates the series representation of y yielding y', substitutes both into the original equation, and expands...
  4. K

    Solving a System of Differential Equations

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  5. D

    Differential equations - backwards problem

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  6. D

    Differential Equations: Bernoulli Equation

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  7. C

    Spring Problem, Differential Equations

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  8. J

    Intro to Differential equations: Vector Spaces

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  9. U

    Runge Kutta for 4 coupled differential equations

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  10. S

    Where does one start with differential equations?

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  11. B

    One Physics MS semester left - what courses to take?

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  12. J

    Rearrange equation (solution of ODE)

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  13. mef51

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  14. J

    Help Solving Differential Equations

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  15. _N3WTON_

    Introductory Differential Equations Textbook

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  16. C

    Integrating ##d\psi=(x+y)dx +x_0dy##

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  17. L

    Info on Bessel functions & their use as basis functions.

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  18. rakeru

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  19. gfd43tg

    Inhomogeneous differential equations

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  20. S

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  21. C

    Differential Equations : Compound Interest

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  22. L

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  23. L

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  24. S

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  25. A

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  26. C

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  27. V

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  28. E

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  29. R

    MHB Asymptotic expansion on 3 nonlinear ordinary differential equations

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  30. W

    Asymptotic expansion on 3 nonlinear ordinary differential equations

    The 3 nonlinear differential equations are as follows \begin{equation} \epsilon \frac{dc}{dt}=\alpha I + \ c (-K_F - K_D-K_N s-K_P(1-q)), \nonumber \end{equation} \begin{equation} \frac{ds}{dt}= \lambda_b P_C \ \epsilon \ c (1-s)- \lambda_r (1-q) \ s, \nonumber \end{equation}...
  31. M

    Please recommend me a good textbook for Differential Equations?

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  32. dkotschessaa

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  33. C

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  34. C

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  35. C

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  36. I

    MHB Modeling with Differential Equations

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  37. A

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  38. I

    MHB Differential equations and initial value problems

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  39. M

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  40. T

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  41. I

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  42. S

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  43. P

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  44. H

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  45. JasonHathaway

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  46. sheldonrocks97

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  47. T

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  48. M

    MHB Mesh Currents with Differential Equations

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  49. L

    Finding Geodesics/Solving Differential Equations

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  50. R

    Stochastic differential equations question. An over view

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