\begin{equation} \begin{cases} u_t=u_{xx}+4u+x^2-2t-4x^2t+2\cos^2(x), x\in (0,\pi) \\ u(x,0)=0 \\ u_x(0,t)=0 \\ u_x(\pi ,t)=2\pi t \end{cases} \end{equation}
I've asked about that PDE yesterday, and got a solution but without using the Fourier Transformation
But we should solve this with the help of the Fourier Transformation
So how should I do it? Because we only did that for
\begin{equation} \begin{cases} u_t=a^2u_{xx}, x\in (0,l) \\ u(x,0)=... \\ u_x(0,t)=... \\ u_x(l ,t)=... \end{cases} \end{equation}
But we cannot apply it to the PDE given because it's not a heat equation in the first place