PDE - heat equaltion with \cos(x)

Question

$$u_t=u_{xx}+\cos(x)$$ $$u(x,0)=e^{2x} \forall x$$ My idea:
First of all if we can remove $\cos(x)$ we will get heat equation. And the heat equation we know how to solve(separation of variables, Fourier method, Poisson formula... ) but question is how to deal with $\cos(x)$?

Answer 1

HINT :

$$u(x,t)=v(x,t)+\cos(x)$$ $$u_{xx}=v_{xx}-\cos(x)$$ $$v_t=v_{xx}$$ $v(x,0)=e^{2x}-cos(x)$