- #1
vipertongn
- 98
- 0
Homework Statement
solve using undetermined coeffecients
y"+3y=-48x^2e^(3x)
Homework Equations
x^2e^3x gives a Yp=(Ax^2+Bx+C)e^3x
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