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. Santilopez10

    Calculus Book for complementing differential equations

    Hello! Currently I own Differential Equations by H.B Phillips, a really old book, but difficult and does it´s purpose. I have only 1 problem, certain exercises require certain geometrical functional study I suppose, for example: "find the equation of the curves so that the part of every tangent...
  2. F

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  3. JTC

    A Causality in differential equations

    Hello, I am studying control theory. And I have encountered something I have never considered or thought about. Consider a system with y as the output differential equation and u as the input. any(n) + ... + a1y(1) + a0y = bmu(m) + ... + b1u(1) + b0u Here, the subscripts indicate...
  4. J6204

    Finding differences amongst a system of differential equations

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  5. D

    Solving 2nd order DE with initial condition

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  6. Spoti112

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  7. Spoti112

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  8. thepikminman

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  9. J6204

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  10. D

    MHB How Can We Convert Higher Order Differential Equations into First Order Systems?

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  11. Ron Burgundypants

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  12. G

    I Symmetry in differential equations

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  13. R

    Coupled differential equations using matrix exponent

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  14. A

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  15. A

    I Solving the differential equations involving SHM

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  16. L

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  17. R

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  18. Jianphys17

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  19. F

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  20. W

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  21. Marcus95

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  22. W

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  23. Saracen Rue

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  24. Saracen Rue

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  26. K

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  27. awholenumber

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  28. Arman777

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  29. C

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  30. A

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  31. kupid

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  32. R

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  33. gelfand

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  34. F

    I Second order DE with Sine function

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  35. patrickmoloney

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  36. cg78ithaca

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  37. M

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  38. R

    I Parameterization by differential equations

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  39. Poetria

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  40. MAGNIBORO

    I Differential Equations For Solving A Recursive equation

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  41. W

    I What differential equations need to be solved more quickly?

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  42. B

    A Test if 2nd order diff eq. can be derived from a Hamiltonian

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  43. M

    Solve Snow Plow Problem: Find Constant k

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  44. G

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  45. A

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  46. I

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  47. S

    I Rescaling the equation of motion of inflation

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  48. J

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  49. Vanessa Avila

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  50. S

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