2.15.23 Plateau \((1+u_y^2)u_{xx} - 2 u_x u_y y_{xy} + (1+u_x^2) u_{yy} = 0\)

problem number 132

Added December 27, 2018.

Taken from https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations

Plateau. Solve for \(u(x,y)\) \[ (1+u_y^2)u_{xx} - 2 u_x u_y y_{xy} + (1+u_x^2) u_{yy} = 0 \]

Mathematica


Failed

Maple


\[u \left (x , y\right ) = c_{7} \left (\tanh ^{3}\left (c_{1}+c_{2} \left (-i y +x \right )\right )\right )+c_{5} \tanh \left (c_{1}+c_{2} \left (-i y +x \right )\right )+c_{4}\]

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