2.1.56 \(y z u_x - x z u_y+ x y (x^2+y^2) u_z=0\) Problem 3.8(d) Lokenath Debnath

problem number 56

Added June 3, 2019.

Problem 3.8(d) nonlinear pde’s by Lokenath Debnath, 3rd edition.

Solve for \(u(x,y,z)\) \[ y z u_x - x z u_y+ x y (x^2+y^2) u_z=0 \]

Mathematica


\[\left \{\left \{u(x,y,z)\to c_1\left (\frac {1}{2} \left (x^2+y^2\right ),\frac {1}{2} \left (-x^2 y^2-x^4+z^2\right )\right )\right \}\right \}\]

Maple


\[u \left (x , y , z\right ) = \mathit {\_F1} \left (x^{2}+y^{2}, -x^{4}-x^{2} y^{2}+z^{2}\right )\]

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