# What is a solution to the differential equation dy/dx=xy?

Jul 4, 2016

$= \alpha {e}^{{x}^{2} / 2}$

#### Explanation:

it's separable!!

$y ' = x y$

$\frac{1}{y} \setminus y ' = x$

$\ln y = {x}^{2} / 2 + C$

$y = {e}^{{x}^{2} / 2 + C}$

$= \alpha {e}^{{x}^{2} / 2}$