# What is a solution to the differential equation dy/dx=x^2y?

Aug 2, 2016

$y = C {e}^{{x}^{3} / 3}$

#### Explanation:

First, separate the variables:

$\frac{\mathrm{dy}}{\mathrm{dx}} = {x}^{2} y \text{ "=>" } \frac{\mathrm{dy}}{y} = {x}^{2} \mathrm{dx}$

Integrate both sides:

$\int \frac{\mathrm{dy}}{y} = \int {x}^{2} \mathrm{dx} \text{ "=>" } \ln \left(y\right) = {x}^{3} / 3 + C$

Solve for $y$:

$y = {e}^{{x}^{3} / 3 + C} = {e}^{{x}^{3} / 3} \left({e}^{C}\right) = C {e}^{{x}^{3} / 3}$