7.1.4 problem number 4

problem number 421

Added January 2, 2019.

Problem 1.4 from Handbook of first order partial differential equations by Polyanin, Zaitsev, Moussiaux.

Solve for $w(x,y)$ $$w_y=wf(x,y)$$

Mathematica ✓

ClearAll["Global`*"]; 
pde =  D[w[x, y], y] == w[x, y]*f[x, y]; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, y], {x, y}], 60*10]];
 

$$\left\{\{w(x,y)\to c_1(x)\exp ({\int }_1^{y}f(x,K[1])dK[1])\}\right\}$$

Maple ✓

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

$$w(x,y)=\mathit{\text{\_F1}}\left(y\right){\mathrm{e}}^{\int f(x,y)dx}$$

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