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Thread: confused on how i'm suppose to prove this DE principal, suppose.. .:Resolved:.

  1. #1

    Thread Starter
    Hyperactive Member voidflux's Avatar
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    Question confused on how i'm suppose to prove this DE principal, suppose.. .:Resolved:.

    Hello everyone,


    I have some notes on the principal of superpostion of solutions for homogenous equations. It sounds comlex but it really isn't. I know how to solve prolems like this but our professor comes out of the blew and says, prove the principal.

    Well it says

    y'' + p(x)y' + q(x)y = 0; <----equation 1
    If y1 and y2 are two solutions of the above equation(1), then
    y = c1y1 + c2y2; //where c1 and c2 are constants
    is also a solution. And i'm suppose to prove that y = c1y1 + c2y2 is also a solution. She said its really simple. She said all we have to do is take the first derivative and 2nd derivative of y = c1y1+c2y2 and then plug that value into the above equation (1). But this confused because if i take the first derivative of y, i would get:

    y' = c1 + c2;
    y'' = 0 + 0;

    what am i supose to do with that mess? after plugging it into the above equation i get no where. Any idea's on how i am suppoe to prove this?

    Thanks!!
    Last edited by voidflux; Sep 23rd, 2004 at 07:24 PM.
    C¤ry Sanchez
    Computer Science/Engineering
    @ Penn State
    IBM.zSeries Intern
    Mandriva 2007

  2. #2
    vbuggy krtxmrtz's Avatar
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    The solutions y1 and y2 are functions, not constants. Therfore, when you take derivatives:

    y' = c1y'1 + c2y'2

    y'' = c1y''1 + c2y''2

    Plug those in along with

    y = c1y1 + c2y2

    and you're done.
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  3. #3

    Thread Starter
    Hyperactive Member voidflux's Avatar
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    Talking

    Thanks again, it worked!
    Last edited by voidflux; Sep 23rd, 2004 at 07:24 PM.
    C¤ry Sanchez
    Computer Science/Engineering
    @ Penn State
    IBM.zSeries Intern
    Mandriva 2007

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