aux + buy = 0 Problem 3.3(b) Lokenath Debnath

2.1.36 $a u_{x} + b u_{y} = 0$ Problem 3.3(b) Lokenath Debnath

problem number 36

Added June 2, 2019.

Problem 3.3(b) nonlinear pde’s by Lokenath Debnath, 3rd edition.

Solve for $u (x, y)$ $a u_{x} + b u_{y} = 0$

Mathematica ✓

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

${{u (x, y) \to c_{1} (y - \frac{b x}{a})}}$

Maple ✓

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

$u (x, y) =_F1 (\frac{y a - b x}{a})$

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2.1.36 aux+buy=0 Problem 3.3(b) Lokenath Debnath

2.1.36 $a u_{x} + b u_{y} = 0$ Problem 3.3(b) Lokenath Debnath