2.1.54 \(x^2 u_x+y^2 u_y+z(x+y)u_z=0\) Problem 3.8(b) Lokenath Debnath

problem number 54

Added June 3, 2019.

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

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

Mathematica


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

Maple


\[u \left (x , y , z\right ) = \mathit {\_F1} \left (\frac {x -y}{x y}, \frac {z}{x y}\right )\]

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