The solution of the differential equation \(\frac{dy}{dx}=\frac{y}{x}\) is

The given differential equation is:

\(\frac{dy}{dx}=\frac{y}{x}.....(I)\)

Rearrange the tems of the equation \(\left(I\right)\)

\(\frac{dy}{y}=\frac{dx}{x}.....(II)\)

Integrate on both sides of equation \((II)\) and calculate the solution of the given differential equation.

\(\int \frac{dy}{y}=\int \frac{dx}{x}\\ \log (y)=\log (x)+\log (c)\\ \log (y)=\log (cx)\\ y=cx\)

Hence, the solution of the given differential equation is \(y=cx\).