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Math Help - Simply 2nd Order ODE question

  1. #1
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    Simple 2nd Order ODE question

    Could someone please help me with this question?


    Find the general solution of the differential equation:

    f''(x) = sin(2x-4)



    Do i simply integrate both sides twice? What method of integration do i use?
    Last edited by remember; July 28th 2011 at 08:52 AM.
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  2. #2
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    Re: Simple 2nd Order ODE question

    Quote Originally Posted by remember View Post
    Could someone please help me with this question?


    Find the general solution of the differential equation:

    f''(x) = sin(2x-4)



    Do i simply integrate both sides twice? What method of integration do i use?
    Hi remember. Welcome to MHF.

    y'' =
    d/dx (y') = sin(2x-4)

    Integrate w.r.t to x:
    \int\,d(y')\,=\int \sin(2x-4)\,dx

    Don't forget your constant of integration.

    Write y' as dy/dx & integrate w.r.t x.
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  3. #3
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    Re: Simple 2nd Order ODE question

    Thanks!

    Also, say for example the DE was changed to this:

    y'' = sin(2x-4) + cos5x

    I take it I just integrate the sin and cos parts of the equation seperately because they are added and not a product of each other?
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  4. #4
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    Re: Simple 2nd Order ODE question

    Quote Originally Posted by remember View Post
    Thanks!

    Also, say for example the DE was changed to this:

    y'' = sin(2x-4) + cos5x

    I take it I just integrate the sin and cos parts of the equation seperately because they are added and not a product of each other?
    Yes.
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