What is a solution to the differential equation dy/dx=3y?

Aug 6, 2016

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

Explanation:

$\frac{\mathrm{dy}}{\mathrm{dx}} = 3 y$

$\frac{1}{y} \frac{\mathrm{dy}}{\mathrm{dx}} = 3$

$\int \setminus \frac{1}{y} \frac{\mathrm{dy}}{\mathrm{dx}} \setminus \mathrm{dx} = \int 3 \setminus \mathrm{dx}$

$\int \setminus \frac{1}{y} \setminus \mathrm{dy} = \int 3 \setminus \mathrm{dx}$

$\ln y = 3 x + C$

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