I want to convert the following 1st order non homogeneous differential equation system into 2nd order differential equation.
So i get $x'_1=x_1+2x_2+2t$ and $x'_2=3x_1+2x_2-4t$
After doing some calculations, I get the following differential equation $x''_1-3x'_1-4x_1-10t=0$ Is this correct? I want to verify it by checking general and particular solution to this 2nd order differential equation. I already have general and particular solution to 1st order differential equation system