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$$ \frac{ \partial^2 u(x,t) }{\partial x^2} = k^2 \frac{ \partial u(x,t) }{\partial t} $$

With boundary conditions.

I use separation variables to find the result, but i dont know how to solve the equation plus a constant:

$$ \frac{ \partial^2 u(x,t) }{\partial x^2} = k^2 \frac{ \partial u(x,t) }{\partial t} + 2 $$

How can i solve the second PDE?