# What is a solution to the differential equation dy/dx=e^x/y with y(0)=1?

Jun 28, 2016

$y = \sqrt{2 {e}^{x} - 1}$

#### Explanation:

$\frac{\mathrm{dy}}{\mathrm{dx}} = {e}^{x} / y$

separate

$y \setminus \frac{\mathrm{dy}}{\mathrm{dx}} = {e}^{x}$

$\int \setminus y \setminus \mathrm{dy} = \int {e}^{x} \setminus \mathrm{dx}$

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

using the IV
${1}^{2} / 2 = 1 + C \setminus \implies C = - \frac{1}{2}$

${y}^{2} = 2 {e}^{x} - 1$ or $y = \sqrt{2 {e}^{x} - 1}$