I am unsure how to approach the added F(x,t) part of this partial differential equation.
$$\begin{cases} \partial_t^2u=\partial_x^2u+F(x,t),& x,t\in\mathbb{R}\,\\ u(x,0)=f(x)\\ \partial_tu(x,0)=g(x)\end{cases}$$
I am unsure how to approach the added F(x,t) part of this partial differential equation.
$$\begin{cases} \partial_t^2u=\partial_x^2u+F(x,t),& x,t\in\mathbb{R}\,\\ u(x,0)=f(x)\\ \partial_tu(x,0)=g(x)\end{cases}$$
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