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$\begin{aligned} & {{u}_{t}}=K{{u}_{xx}}+g(t),\text{ }0<x<L,\text{ }t>0, \\

& {{u}_{x}}(0,t)={{u}_{x}}(L,t)=0,\text{ }t>0 \\

& u(x,0)=f(x), \\

\end{aligned}

$

a) Show that $v=u-G(t)$ satisfies the initial value boundary problem where $G(t)$ is the primitive of $g(t)$ with $g(0)=0$

b) Find the solution when $g(t)=\cos wt$ and $f(x)=0.$

__Attempts__:

Okay so I have $g(t)=\displaystyle\int_0^t G(t)\,ds,$ is that how do I need to proceed?