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

Oct 4, 2016

$\left\mid y \right\mid = C {e}^{k x}$

#### Explanation:

Assiuming k is just some constant, this is immediately separable

$\frac{1}{y} y ' = k$

And
$\int \left(\frac{1}{y} y ' = k\right) \mathrm{dx}$

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

$\implies \ln \left\mid y \right\mid = k x + C$

$\left\mid y \right\mid = {e}^{k x + C} = C {e}^{k x}$