2.1.53 \(x u_x+y u_y+z u_z=0\) Problem 3.8(a) .Lokenath Debnath

problem number 53

Added June 3, 2019.

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

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

Mathematica

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

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

Maple

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

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

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