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Analytically solve partial differential equation?

Gaurav Kumar
Posted 6 years ago

I have to solve this PDE analytically. I am giving the input as shown in the image but when I am moving forward, there is no solution generated. Why? Do I need to give any more input?! Mathematica Screenshot

Equation = 
  D[\[Psi][x, y], {x, 2}] + 
    D[\[Psi][x, y], {y, 2}] == \[Kappa]^2*((2*Sinh[\[Psi][x, y]])/(
     1 + \[Nu]*Sinh[\[Psi][x, y]]^2));

DSolve[Equation, \[Psi][x, y], {x, y}]
POSTED BY: Gaurav Kumar
3 Replies
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When Mathematica returns the input as the output, it means that the calculation returned unevaluated. This often means that the function does not have the methods available to solve the problem symbolically, or it is mathematically impossible to obtain a symbolic solution (not all sums, integrals, or differential equations have symbolic solutions after all).
POSTED BY: Mariusz Iwaniuk
Gaurav Kumar
Gaurav Kumar
Posted 6 years ago

So what if I try NDSolve command with certain boundary conditions?
POSTED BY: Gaurav Kumar

Welcome to Wolfram Community! Please make sure you know the rules: https://wolfr.am/READ-1ST

The rules explain how to format your code properly. If you do not format code, it may become corrupted and useless to other members. Please EDIT your post and make sure code blocks start on a new paragraph and look framed and colored like this.

int = Integrate[1/(x^3 - 1), x];
Map[Framed, int, Infinity]

enter image description here
POSTED BY: EDITORIAL BOARD
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