Partial Differential Equation is:
$$\frac{∂u}{∂t} = \frac{∂^2u}{∂x^2}$$
Where $t>0$, and $0<x<1$.
With the boundary conditions:
$$u(0,t)=1$$
$$u(1,t) = 1$$
and the initial conditions:
$$u(x,0) = 1+\sin{(πx)}$$
I'm trying to solve this by using Laplace transform but I couldn't.
Best Answer
You haven't even bothered to ask a question. Good effort.
Here is a list of examples for your problem. Example 3 is something very similar to what you are trying to do. If I was you - Be able to understand all three examples before trying the one you've posted, otherwise you won't get it. Good Luck! Post your attempts if you get stuck and we can help.