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

Aug 2, 2016

$y = C x$

#### Explanation:

We can separate the variables:

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

Integrate both sides:

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

So:

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