Find a formula for the solution to $$ \begin{cases} w_t−kw_{xx}=f(x,t) &\text{for } x>0,t>0\\ w(x,0)=g(x) &\text{for } x>0\\ w_x(0,t)=h(t) &\text{for } t>0\\ \end{cases}$$ Hint: What system does $(,)=(,)−ℎ()$ satisfy?
I know I have to use either odd or even extension to find the solution for this heat equation with source, but I don't understand how to use the Hint given in my proof.
Any help would be appreciated!