What is a solution to the differential equation $\frac{d y}{d x} = x e^{y}$ $dy/dx=xe^y$ ?

Question

13740 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-29T20:36:36

$y = ln (\frac{1}{C - \frac{x^{2}}{2}})$ $y = ln (1/(C - x^2/2))$

$y' = xe^y$

$e^(-y)y' = x$

$int e^(-y)y' dx =int x dx$

$int e^(-y) dy =int x dx$

$-e^(-y) =x^2/2 + C$

$e^(-y) =C - x^2/2$

$-y =ln (C - x^2/2)$

$y =- ln (C - x^2/2)$

$y = ln (1/(C - x^2/2))$

What is a solution to the differential equation dy/dx=xe^ydydx=xeydy/dx=xe^y?