# What is a solution to the differential equation dy/dx=4y?

Aug 2, 2016

$y = C {e}^{4 x}$

#### Explanation:

We can separate the variables:

$\frac{\mathrm{dy}}{\mathrm{dx}} = 4 y \text{ "=>" } \frac{\mathrm{dy}}{4 y} = \mathrm{dx}$

Integrate both sides:

$\int \frac{\mathrm{dy}}{4 y} = \int \mathrm{dx} \text{ "=>" "1/4intdy/y=intdx" "=>" } \frac{1}{4} \ln \left(y\right) = x + C$

Solving for $y$:

$\ln \left(y\right) = 4 x + C \text{ "=>" } y = {e}^{4 x + C} = {e}^{4 x} \cdot {e}^{C} = C {e}^{4 x}$