I am trying to solve the following complicated second-order PDE
eqn =
(D[D[U[x, y], x], x] - 1/x D[U[x, y], x] - 1/x D[D[U[x, y], y], y])^2 +
4(-D[1/x D[U[x, y], y], x])^2
==
(2 C q + (D[D[U[x, y], x], x] + 1/x D[U[x, y], x] +
1/x^2 D[D[U[x, y], y], y]) p)^2;
DSolve[eqn, U[x, y], {x, y}]
where p
, q
and C
are the constant values.
Unfortunately, Mathematica doesn't solve the equation and just returns the DSolve
expression unevaluated. Any idea or comments to solve the equation would be appreciated.
DSolve
attempts to solve differential equations by applying known methods. It is not able to develop and employ previously unknown methods. Sadly, it also sometimes fails to solve differential equations even when they can be solved by known methods. $\endgroup$ – bbgodfrey Sep 1 '18 at 1:35