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1)D^2(D-1)y=3e^x+sinx

for yc:

let y=e^mx

D^2(D-1)e^mx=0

m^2(m-1)e^mx=0

f(m)=0

m^2(m-1)=0

m=0,0,1

yc= C1+C2x+C3e^x

for yp:

R(x)=3e^x+sinx

m'=1,+/- 1i

yp=Axe^x+Bcosx+Csinx

yp'=A(xe^x+e^x)-Bsinx+Ccosx

yp"=A(xe^x+2e^x)-Bcosx-Csinx

D^2(D-1)yp=3e^x+sinx

Guys can you help me find the value of A, B and C. I had a hard time simplifying the terms and can't equate the coefficients. Thanks for analyzing my post this far. :D

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# Homework Help: Solution of a nonhomogeneous equation

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