What is Differential equations: Definition and 999 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. E

    Engineering Solving RLC circuit using differential equations

    Homework Statement Find the full response. Assume Vin is a squarewave with Vpp =10V and Vamp = +5V Homework Equations KCL The Attempt at a Solution My teacher gave this solution but I don't really understand some parts of it. Full response = Natural response + forced response Thevenin...
  2. E

    Engineering Solve OpAmp Circuit Using Differential Equations

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  3. Q

    Identifying Types of Singularity in Differential Equations

    Homework Statement Identify the type of singularity at x=0 for these differential equations x*Sin[1/x]*y''[x]+y[x]==0 x^2*y''[x]+Sin[1/x]*y[x]==0 Homework Equations A Singular point is regular if f(x)(x-x_0)^n is defined as x approaches x_0 and is analytic in a near a neighborhood of that...
  4. ShayanJ

    A Differential equations without Green functions

    Are there differential equations that, for some reason, don't have a Green function? Are there conditions for a DE to satisfy so that it can have a Green function? Thanks
  5. H

    MHB Differential equations stability

    A one-dimensional dynamical system is given by $x′ = f(x), t \in [0,+\infty)$, where $f : \mathbb{R} \to \mathbb{R}$ is the smooth function defined as follows: $$f(x) = \begin{cases} x^4 \sin \left(\frac{1}{x}\right) & x \neq 0\\ 0 & x = 0. \end{cases}.$$ Find all the equilibrium points and...
  6. TheSodesa

    A real parameter guaranteeing subspace invariance

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  7. M

    Physicists' knowledge of differential equations

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  8. H

    Arbitrary constant in denominator

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  9. DarkBabylon

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  10. W

    Linear Differential Equations and Linear Operator Problem

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  11. Elvis 123456789

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  12. Pouyan

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  13. Phylosopher

    Courses Differential equations theory course, is it useful?

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  14. T

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  15. J

    Help finding general solution for 2nd order linear DE

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  16. J

    I What's the geometric interpretation of the trace of a matrix

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  17. jdawg

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  18. C

    Establishing equations for a worm screw mechanism

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  19. tomwilliam2

    I Solving linear differential equations

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  20. RoboNerd

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  21. F

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  22. J

    A Free damped vibration of a system of 2 dof, demostration

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  23. awholenumber

    Calculus First order differential equations ?

    what is a good book to learn first order differential equations ??
  24. awholenumber

    I First order differential equations ?

    what is a good book to learn first order differential equations ??
  25. awholenumber

    I Differential equations and numerical methods questions

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  26. Houeto

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  27. F

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  28. dumbdumNotSmart

    B System of differential equations Basic question

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  29. B

    I Laplace transform using differential equations

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  30. J

    I William skinner Machine gravity

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  31. J

    An application of free fall (DE) model to industry

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  32. awholenumber

    B Few basic questions about differential equations....

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  33. H

    I How to find the inverse of an integral transform?

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  34. Dusty912

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  35. chwala

    Finding Stationary Points for the Differential Equation y=(lnx)^2/x

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  36. J

    Is there an encyclopedia of DE that accepts solutions?

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  37. R

    Video lectures for differential equations 2

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  38. A

    B Complex Replacement: Justification?

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  39. faradayscat

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  40. faradayscat

    I Non-homogeneous systems with repeated eigenvalues

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  41. T

    How to prepare for differential equations?

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  42. R

    Transient heat transfer in a sphere

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  43. faradayscat

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  44. Dusty912

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  45. D

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    Homework Statement dx/dt + dy/dt = 2x + 2y + 1 dx/dt + 2(dy/dt) = y + 3 Homework Equations The Attempt at a Solution Dx + Dy = 2x + 2y + 1 Dx + 2Dy = y + 3 --Rearranging---------------------------- Dx - 2x = -Dy + 2y + 1 Dx = -2Dy + y + 3 ---Factoring----------------------------- (D...
  46. E

    A Nonhomogeneous second order nonlinear differential equations

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  47. kostoglotov

    Why are these capacitor voltages opposite polarity?

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  48. The Bill

    Analysis General texts on systems of partial differential equations?

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  49. Poetria

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  50. E

    I Question about using matrices for differential equations

    Let x(t)= [x1(t) x2(t)] be a solution to the system of differential equations: x′1(t)=−2x1(t)+2x2(t) x′2(t)==−6x1(t)+9x2(t) If x(0)= [4 -2] find x(t). I got the eigenvalues to be -6 and -5, but I don't know how to calculate the coefficients in front of the exponents. For lambda=-6 I get...
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