# What is a solution to the differential equation e^ydy/dt=3t^2+1?

Jul 1, 2016

$y = {\log}_{e} \left({t}^{3} + t + C\right)$

#### Explanation:

${e}^{y} \frac{\mathrm{dy}}{\mathrm{dt}} = 3 {t}^{2} + 1$ grouping variables
${e}^{y} \mathrm{dy} = \left(3 {t}^{2} + 1\right) \mathrm{dt} \to {e}^{y} = {t}^{3} + t + C$

Finally

$y = {\log}_{e} \left({t}^{3} + t + C\right)$