What is Differential: Definition and 1000 Discussions

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

    Engineering First order differential equations (movement of a rotary solenoid)

    My question i am trying to solve: I have successfully done first order equations before but this one has got me a little stuck. My attempt at the general solution below: $${5} \frac{\text{d}\theta}{\text{d}t}=-6\theta$$ $${5} \frac{\text{d}\theta}{\text{d}t} =\frac{\text{-6}\theta}{5}$$...
  2. Pouyan

    Interpreting Statistical Questions: Ice Hockey Player Diff.

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  3. chwala

    Proof involving ##ω(ξ,n)=u(x,y)## - Partial differential equations

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  4. Anava1001

    A Normalized differential cross section

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  5. M

    From differential equations to transfer functions

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  6. D

    Finding the differential equation of motion

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  7. The Bill

    Applied Resources for general vector differential equations?

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  8. TheSpectacularSpecs

    I Surface Differential Rotation by measuring the position of sunspots

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  9. mcastillo356

    Foundations On how to best introduce the concept of differential in Physics

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  10. MichaelBack12

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  11. S

    Classification of a second order partial differential equation

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  12. A

    Domain of definition differential equations

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  13. V

    I Limit cycles, differential equations and Bendixson's criterion

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  14. pellman

    I What is differential about differential forms?

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  15. J

    I Integral-form change of variable in differential equation

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  16. chwala

    Solve the first order differential equation

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  17. L

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  18. Somaiyah

    Help with deciding electives: Differential Geometry or Quantum Info

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  19. chwala

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  20. K

    I Definition of order of a partial differential equation

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  21. W

    A Solving nonlinear singular differential equations

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  22. cianfa72

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  23. chwala

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  24. M

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  25. cianfa72

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  26. B

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  27. galaxywanderer

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  28. Z

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  29. KyleGranger

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  30. A

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  31. A

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  32. W

    I Nonlinear differential equation

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  33. MichPod

    A A better notation for a differential?

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  34. A

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  35. M

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  36. J

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  37. J

    Is the magnetic field B→. a state function and exact differential?

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  38. Istiak

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  39. S

    MHB Solve Differential Eq: xe^-1/(k+e^-1) for x, k, t

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  40. L

    I Solve second order linear differential equation

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  41. M

    I Dependency of phase space generator to differential distributions

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  42. Leo Liu

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  43. 1

    Biology Why do these biology textbooks write 'differential' as an adjective?

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  44. A

    MHB Question about the differential in Calculus

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  45. Poetria

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  46. N

    B Basic Idea of Differential Equations

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  47. agnimusayoti

    How to Measure Very Small Differential Pressure in a Subsonic Wind Tunnel

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  48. Falgun

    Geometry Confusion about Differential Geometry Books

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  49. K

    I An attempt to find the total differential of a two-variable function

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  50. stevendaryl

    A Differential equation for affine parameter

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