(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

solve using undetermined coeffecients

y"+3y=-48x^2e^(3x)

2. Relevant equations

x^2e^3x gives a Yp=(Ax^2+Bx+C)e^3x

3. The attempt at a solution

I can get yc easily which is yc=cos(sqrt(3x))+sin(sqrt(3x))

However, I'm not sure as to how to set it up so that -48x^2e^(3x) and the yp. the -48 is throwing me off. If I make it so then that is equivalent to a constant D in teh equation I get

Yp= De^3x(Ax^2+Bx+C)

taking to the second derivative

Yp"+3Yp=3D[(10Ax^2e^2x)+(18Axe^3+7Bxe^3x)+(6Ae^3x+9Be^3x+6Ce^3x)=-48x^2e^(3x)

At most I could get D=-16

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# Superposition approach

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