2.1.55 \(x(y-z)u_x+y(z-x)u_y+z(x-y)u_z=0\) Problem 3.8(c) Lokenath Debnath

problem number 55

Added June 3, 2019.

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

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

Mathematica


\[\{\{u(x,y,z)\to c_1(-x y z,x+y+z)\}\}\]

Maple


\[u \left (x , y , z\right ) = \frac {c_{4} c_{5} x^{c_{2}} y^{c_{2}} z^{c_{2}} {\mathrm e}^{c_{2}} {\mathrm e}^{-c_{1} x} {\mathrm e}^{-c_{1} y} {\mathrm e}^{-c_{1} z}}{c_{3}}\]

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