So I have this question where I need to find $u(x,t)$ such that:
$$ u_{tt}-c^{2}u_{xx}=x+ct; -\infty<x<\infty\\ u(x,0)=\sin x \\ u_{t}(x,0)=x^{2} $$
The instructor mentioned it would be "easy" if I used change of variables, but my T.A. told me that I should memorize Duhamel's principle. Is there any way around using Duhamel's principle or is my T.A. correct? I'm really confused because I don't remember going over Duhamel's in lecture.
