Hello everyone! so I want to know how to plot/(get the answer also) to this Second order partial differential equation on mathematica, I can't seem to get the input right. So I was able to input the data for the Laplace equation (see first attachment), and it goes like this:

LaplaceEquation = D[u[x, y], {x, 2}] + D[u[x, y], {y, 2}] == 0;

bc = {u[0,y] == 0, u[x, 0] == 0, u[L, y]== 0, u[x, L] == f[x]};

DSolve[{LaplaceEquation,bc}, u[x, y], {x, y}]

AND! I did got the answer, now I have to do the same with a very similar problem, the problem is that the boundary conditions change, and I don't know how to input those (see attachment 2), so now my new boundary conditions are:

Solve: Uxx + Uyy = 0 for 0 < x < L and 0 < y < L

At x = 0, dU/dx = 0

At y = 0, U = 0

At x = a, dU/dx = 0

At y = b, U = f(x)

As you can figure, the problem is inserting the derivativs dU/dx in the boundary conditions I don't really know how to do that, before my boundary conditions were:

Solve: Uxx + Uyy = 0 for 0 < x < L and 0 < y < L

At x = 0, U = 0

At y = 0, U = 0

At x = L, U = 0

At y = L, U = f(x)

and I did it fine, now I am not sure how to do it, please help!

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