6.1.4 problem number 4

problem number 419

Added January 2, 2019.

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

Solve for \(w(x,y)\) \[ w_y = w f(x,y) \]

Mathematica


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

Maple


\[w \left (x , y\right ) = \mathit {\_F1} (y ) {\mathrm e}^{\int f \left (x , y\right )d x}\]

________________________________________________________________________________________