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

problem number 57

Added June 3, 2019.

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

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

Mathematica ✗

ClearAll["Global`*"]; 
pde =  x*(y^2-z^2)*D[u[x, y,z], x] +y*(z^2-y^2)*D[u[x, y,z], y]+z*(x^2-y^2)*D[u[x, y,z], z]== 0; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde ,u[x, y,z], {x, y,z}], 60*10]];
 

Failed

Maple ✗

restart; 
pde :=x*(y^2-z^2)*diff(u(x,y,z),x) + y*(z^2-y^2)*diff(u(x,y,z),y)+z*(x^2-y^2)*diff(u(x,y,z),z)= 0; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y,z))),output='realtime'));
 

sol=()

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