I What is the solution to the heat equation with a constant added?

[morenopo2012]

I have seen how to solve the heat equation:

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

With boundary conditions.

I use separation variables to find the result, but i don't 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?

 

[Chestermiller]

I have seen how to solve the heat equation:

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

With boundary conditions.

I use separation variables to find the result, but i don't 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?

Write $$u=U+V$$ where V satisfies the equation:
$$\frac{d^2V}{dx^2}=2$$
subject to the boundary conditions on u. See what that gives you for U.