# What is a solution to the differential equation dy/dt=e^t/(4y)?

Sep 16, 2016

$y = \pm \sqrt{\frac{1}{2} {e}^{t} + C}$

#### Explanation:

$\frac{\mathrm{dy}}{\mathrm{dt}} = {e}^{t} / \left(4 y\right)$

we separate it

$4 y \frac{\mathrm{dy}}{\mathrm{dt}} = {e}^{t}$

we integrate: $\int \left(4 y \frac{\mathrm{dy}}{\mathrm{dt}} = {e}^{t}\right) \mathrm{dt}$

$\implies \int 4 y \mathrm{dy} = \int {e}^{t} \mathrm{dt}$

$\implies 2 {y}^{2} = {e}^{t} + C$

$y = \pm \sqrt{\frac{1}{2} {e}^{t} + C}$