Heat equation plus a constant

  • #1
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 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?
 

Answers and Replies

  • #2
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4,822
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 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?
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.
 

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