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Math Help - Another Undetermined Coefficient question

  1. #1
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    Another Undetermined Coefficient question

    y" + y' = 3x^2

    Here's the work I've done:

    yc:

    1. r^2 + r = 0
    2. r(r + 1) = 0
    3. r=0, -1
    4. Thus, yc= c1 +c2e^-x

    How do I solve for yp? Thanks,

    JN
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Jim Newt View Post
    y" + y' = 3x^2

    Here's the work I've done:

    yc:

    1. r^2 + r = 0
    2. r(r + 1) = 0
    3. r=0, -1
    4. Thus, yc= c1 +c2e^-x

    How do I solve for yp? Thanks,

    JN
    To solve for y_p, we assume it takes on the form of a second degree polynomial : y_p=Ax^2+Bx+C

    Now plug y_p into the DE and solve for the unknown coefficients:

    y_p^/=2Ax+B
    y_p^{//}=2A

    Therefore, we have:

    2A+2Ax+B=3x^2

    Comparing the coefficients, we have:

    \begin{aligned}<br />
2A+B &=0 \\<br />
2A&=0<br />
\end{aligned}<br />

    This implies that both A and B equal \color{red}\boxed{0}.

    Therefore, \color{red}\boxed{y_p=0}.
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