DSolve not working for given system

Questions
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1

So, I’m a beginner on wolfram matematica and I have a problem. Expected result must be the solution of Cauchy’s Problem. Instead it just repeats my input. Can you please help me?

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2

Looks like Mathematica can’t solve, even Maple have problem to solve.

See here Solving partial differential equations in Maple and Mathematica.

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3

I am not sure about the conditions: why “0” and x->“0” with quotation?

su["0", y] == 1/Cosh[y], D[su[x, y], x] == 0 /. x -> "0".

I replaced the quotations and the PDE can be solved

su[0, y] == 1/Cosh[y],
D[su[x, y], x] == 0

Complete code:

dsol = DSolve[
  {
   y*(D[su[x, y], {x, 2}] - D[su[x, y], {y, 2}]) - 
     2 x*D[su[x, y], x, y] - D[su[x, y], y] == 0,
   su[0, y] == 1/Cosh[y],
   D[su[x, y], x] == 0
   },
  su,
  {x, y}]
Plot3D[su[x, y] /. dsol, {x, -3, 3}, {y, -3, 3}]
4

Woah, thanks! The " " came from another language syntaxis, and because wolfram matematica interpreted 0 as “True” for some reason.

5

Hi Maxim,

From reading your post, I believe you are trying to assert the boundary condition that D[su[x, y], x] == 0 when x == 0. I think Masiusz implemented that. However, I believe Sangdon Lee implemented the condition that D[su[x, y], x] == 0 everywhere, which is quite different.

Kind regards,

David