Question

Solve the following differential equation.
$y-x\frac{dy}{dx}=0$.

Answer 1

$y-x\frac{dy}{dx}=0$

$y=x\frac{dy}{dx}$

$\frac{dx}{x}=\frac{dx}{dy}$

Integrate both the sides

$\int \frac{dx}{x}=\int \frac{dy}{y}$

$\frac{-1}{x^2}+c_1=\frac{-1}{y^2}+c_2$

$\frac{1}{y^2}-\frac{1}{x^2}+c=0$