2.1.22 Clairaut equation. \(u = x u_x+ y u_y + \sin ( u_x + u_y )\)

problem number 22

Taken from Mathematica DSolve help pages

Another example of nonlinear Clairaut equation

Solve for \(u(x,y)\) \[ u = x u_x+ y u_y + \sin ( u_x + u_y ) \]

Mathematica


\[\{\{u(x,y)\to c_1 x+c_2 y+\sin (c_1+c_2)\}\}\]

Maple


\[u \left (x , y\right ) = x \mathit {\_c}_{1}+y \mathit {\_c}_{2}+\sin \left (\mathit {\_c}_{1}+\mathit {\_c}_{2}\right )\]

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