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I have the non homogeneous de 4y" + 4y' + y = 3*x*e^x, which also has some inital conditions y(0)=0 and y'(0)=0. but i only need help with getting the particular solution.

Tried method of constant coefficients and it didnt want to work for me.

I end up using: y(p) = A*t*e^t which doent seem right when i substitute in y'(p) and y"(p) into the original equaltion.

Tried method of variation of parameters and i dont think that worked either as in the end i got y(p) = 0.

So far i get the auxilary eq: r^2 + r + 1/4 = 0

=>(r + 1/2) = 0

thus r1 = r2 = -1/2

so y(h) = c1*e^-1/2*t + c2*t*e^-1/2*t

i just need help as to what method i would use to get a the particular solution y(p). from there its gravy :)

thanks in advance