2.16.1 \(S S_{xy} + S_x S_y = 1\)

problem number 140

Taken from Maple pdsolve help pages, problem 4. A second order PDE

Solve for \(S \left ( x,y \right ) \)

\[ S S_{xy} + S_x S_y = 1 \]

Mathematica ✗

ClearAll["Global`*"]; 
pde =  s[x, y]*D[s[x, y], x, y] + D[s[x, y], x]*D[s[x, y], y] == 1; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, s[x, y], {x, y}], 60*10]];
 

Failed

Maple ✓

restart; 
pde := S(x,y)*diff(S(x,y),y,x) + diff(S(x,y),x)*diff(S(x,y),y) = 1; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,S(x,y),'build')),output='realtime'));
 

\[S \left (x , y\right ) = \operatorname {RootOf}\left (\textit {\_Z}^{2}-2 f_{1} \left (y \right )-2 y x -f_{2} \left (x \right )\right )\]

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