# Solve Differential Equation dy/dx=y/x

In this tutorial we shall evaluate the simple differential equation of the form $\frac{{dy}}{{dx}} = \frac{y}{x}$, we shall use method of separating the variables.

Given differential equation of the form

Separating the variables, the given differential equation can be written as

By separating the variable technique we must keep the terms $dy$ and $dx$ in the numerators with their respective functions.
Now integration both sides of the equation (i), we have

Using the formula of integration $\int {\frac{1}{x}dx = \ln x + c}$, we get

Cancelling logarithm from both sides of the above equation, we get

Which is the required solution of the given differential equation.