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Math Help - Question: what kind of diff. eq is that?

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    Question: what kind of diff. eq is that?



    What kind of diff.eq. is that? I don't have any idea from where to begin with
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  2. #2
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    Quote Originally Posted by JrShohin View Post


    What kind of diff.eq. is that? I don't have any idea from where to begin with
    The solution to the equation,
    y'' + y = 0
    Is given by y=c_1\sin x + c_2\cos x

    Here you have the equation,
    y''+y = x
    Thus you need to find a particular solution.
    By inspection it is easy to see that y=x works.

    Thus, the full solution is y=c_1\sin x + c_2\cos x + x
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  3. #3
    Newbie Black Kawairothlite's Avatar
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    this is a second grade ordinary differential equation and you solve it by getting the characteristic equation which in this case is:

    m^2+1=0

    then

    m=\sqrt{-1}= i (+ or - )

    and then you gotta use the standard solutions for complex numbers and u will get:

    <br /> <br />
y=c_1\sin x + c_2\cos x<br /> <br />

    but this is the general solution of the eq. so u gotta apply the parameters variation method or the undefined coefficient method to get the particular solution or also by inspection as the mod said

    Last edited by Black Kawairothlite; October 28th 2008 at 09:22 AM.
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