How to solve a PDE with an additional condition

Question:How to solve a PDE with an additional condition

Posted: Franziska Feher 1

February 24 2011

How can I solve the following problem using Maple:

Determine the special solution u(x,y) of the PDE

( diff(u(x,y),x) )^2+( diff(u(x,y),y) )^2 = u(x,y)

such that the solution passes through the circle

x(s)=cos(s), y(s)=sin(s), z(s)=1 (0 ≤ s ≤ 2π) .

The solution obtained "by hand", i.e. without Maple, reads

u(x,y) = (1/4) ( 1+ $sqrt(x^2+y^2)$ )²

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