# What is a solution to the differential equation dy/dx=3x^2e^-y?

Jul 14, 2016

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

#### Explanation:

$\frac{\mathrm{dy}}{\mathrm{dx}} = 3 {x}^{2} {e}^{-} y$

separate it

${e}^{y} \frac{\mathrm{dy}}{\mathrm{dx}} = 3 {x}^{2}$

$\int \setminus {e}^{y} \frac{\mathrm{dy}}{\mathrm{dx}} \setminus \mathrm{dx} = \int \setminus 3 {x}^{2} \setminus \mathrm{dx}$

$\int \setminus {e}^{y} \setminus \mathrm{dy} = \int \setminus 3 {x}^{2} \setminus \mathrm{dx}$

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

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