I Heat equation plus a constant

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?
 
19,274
3,817
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.
 

Want to reply to this thread?

"Heat equation plus a constant" You must log in or register to reply here.

Related Threads for: Heat equation plus a constant

  • Posted
Replies
3
Views
998
  • Posted
Replies
3
Views
1K
  • Posted
Replies
4
Views
2K
  • Posted
Replies
3
Views
2K
  • Posted
Replies
1
Views
2K
  • Posted
Replies
6
Views
2K
  • Posted
Replies
12
Views
3K
  • Posted
Replies
6
Views
3K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top