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. ATY

    Elliptic partial differential equation

    Hey guys, so my professor told me to take a look at an equation, because he thinks that there is a mistake. We are basically talking about exercise 6.3 (on last image). The pictures will show you the text, so that you have all the information, that I have http://puu.sh/mrNDl/ec19cdff63.png...
  2. P

    Why differential equations? When to use them?

    Hello everyone, I have some questions that have been bothering me for years now. Why do we use differential equations? When would I normally think about using one? What would make me use one? I know it means the slope of a function and I know the derivation/integration rules + the solution of...
  3. G

    Deriving hermite differential equation from schrødinger harm oscillator

    Homework Statement I am trying to obtain the hermite polynomial from the schrødinger equation for a har monic oscillator. My attempt is shown below. Thank you! The derivation is based on this site: http://www.physicspages.com/2011/02/08/harmonic-oscillator-series-solution/ The Attempt at a...
  4. G

    Why 2nd order differential equation has two solutions

    Hello. I forgot the reason why 2nd order differential equation has two independent solutions. (Here, source term is zero) Why 3 or 4 independent solutions are not possible? Please give me clear answer.
  5. V

    Geometry Spivak's differential geometry vs calculus on manifolds

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  6. M

    Rotations in differential geometry

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  7. Alexiy

    Find the differential equation and velocity

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  8. L

    Differential equation mixing problem

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  9. I

    What are differential equations good for?

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  10. j3dwards

    2nd order differential equation (nonhomogenous)

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  11. J

    What kind of differential equations one must know for QM?

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  12. F

    Topology Learn Differential Geometry: Books for Bachelor in Geometric Quantization

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  13. W

    Bungee jump -> differential equation -> simulink simulation

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  14. F

    Solving a first order differential equation

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  15. S

    I First Order Differential Equation

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  16. C

    How do differential equations relate to traffic flow?

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  17. N

    MHB Differential equation y/(x^2+y^2)

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  18. M

    MHB What are the practical applications of differential geometry?

    Hey! :o In what jobs is differential geometry applied and needed?
  19. P

    Nonlinear differential equation

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  20. A

    Solving Second Order Linear Diff Eqns: Proving Theorems & More

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  21. Mr Davis 97

    Absolute value in a differential equation

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  22. T

    A Opposite "sides" of a surface - Differential Geometry.

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  23. N

    MHB Solve the differential equation

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  24. Schwarzschild90

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  25. 1

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  26. 1

    A question about differential form

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  27. D

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  28. R

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  29. J

    Applied Any books on Ordinary Differential Equations w/ applications

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  30. B

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  31. L

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  32. engnrshyckh

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  33. dumbdumNotSmart

    Simple differential equation - Finding the solution

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  34. MidgetDwarf

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  35. N

    Linear algebra and differential equations advising

    Hey guys, I'm talking to my advisor soon and I was wondering if it is typical to, after taking multi variable calc, to take differential equations and linear algebra simultaneously? I'm going to have to be taking both modern physics and organic chemistry II as well, for context. Thanks everyone
  36. L

    Ordinary differential equations. Series method.

    Question: Why equations x(1-x)\frac{d^2y}{dx^2}+[\gamma-(\alpha+\beta+1)x]\frac{dy}{dx}-\alpha \beta y(x)=0 should be solved by choosing ##y(x)=\sum^{\infty}_{m=0}a_mx^{m+k}## and not ##y(x)=\sum^{\infty}_{m=0}a_mx^{m}##? How to know when we need to choose one of the forms. Also when I sum over...
  37. S

    Calculus Good book on differential equations

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  38. M

    MHB System of differential equations

    Hey! :o When we have a system of differential equations $$\bigwedge_{j=1}^n L_j y=f_j$$ is it possible that we reduce it into one differential equation $Ly=f$ so that the system has a solution iff the differential equation $Ly=f$ has a solution? (Wondering)
  39. C

    MHB Stochastic differential equations

    Hello to all, I am a new member, but I've been reading and getting help from this forum for a year! I recently started to study about stochastic calculus because I am considering risk management/ actuarial/ finance job. I would appreciate your help. If we have Poisson $(\lambda)$ and $W$...
  40. A

    Effect of changing differential

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  41. P

    Differential Equation with Bessel Function

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  42. J

    Given the solution find the differential equation

    Homework Statement For each Set write the differential equation they are a solution to. It is also asked to find the wronskian but I remember how to do that. (I am doing this on my own to brush up before I have to take mathphys next semester) 1. e-x,e-4x 2, 1,x,x2 Homework EquationsThe Attempt...
  43. MidgetDwarf

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  44. C

    Newtonian gravity and differential equations

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  45. THE HARLEQUIN

    Gauss' Differential law intuition

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  46. J

    Determine coefficients of a differential equation

    Hi there. I've been struggling with this problem for days now (4 days, no joke) and I feel like I have a mental block and really cannot get any further. I have a system that's described by f(t) = g''(t) + 15g'(t) + 1600g(t) Where the input is g(t) The problem is to, with this information...
  47. C

    Pressure Testing (furnace installation leak)

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  48. E

    Solve coupled nonlinear differential equations

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  49. R

    Fin/Extended surface differential equation for temperature

    I'm trying to deduce the differential equation for temperature for a triangular fin: I know that for a rectangular fin, such as: I can do: Energy entering the left: q_x= -kA\frac{dT(x)}{dx} Energy leaving the right: q_{x+dx} = -kA\frac{dT(x)}{dx} - kA\frac{d² T(x)}{dx²}dx Energy lost by...
  50. Tzabcan

    What did I do wrong in solving this basic differential equation?

    I have this basic differential equation du/dt=(u^2)*(sin t) This is obviously a separable diff eq. So what I've done is: g(t) = sin t h(u) = u^2 1/(u^2) du = sin t dt Integrating both side... 1/y = - cos t + c therefor y = - 1/(cos t + c)Which is wrong, there isn't supposed...
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