Try .The problem is

x''+5x'+6x=3e^(-2t)+e^3t

The homogeneous solution, that I solved is,

x(h)=A(1)e^(-3t)+A(2)e^(-2t)

my problem is when I split it to find the first particular solution, for 3e^(-2t)

I assume

x=B(1)e^-2t

x'=-2B(1)e^-2t

x''=4B(1)e^-2t

I substitute into the original and get

e^(-2t)[4B(1)-10B(1)+6B(1)]=3e^(-2t)

which reduces too

4B-10B+6B=3

This is trivial

any help would be greatly appreciated.

Thank you