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Math Help - differential equations

  1. #1
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    differential equations

    When told to show that something is a solution of a differential equation, then asked to determine the general solution, how do I do it?
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: differential equations

    It depends, to solve some types of differential equations you need an obvious solution. Can you show the differential equation you need to solve?
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  3. #3
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    Re: differential equations

    Unless you are given other information, there is no way to go from a given solution to the general solution.

    Now, if the differential equation is linear second order equation you can use a given solution to reduce to a first order equation and solve that for a second, independent, solution and so write the general solution as a linear combination of the two solutions.
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  4. #4
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    Re: differential equations

    For example, show that y = x is a solution of the equation (1 - x^2)d^2y/dx^2 + (2x)dy/dx - 2y = 0

    I can show that y = x is a solution, but then they ask me to find the general solution of the equation
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