Question

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

Answer 1

Solution :

The given differential equation is

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

$\implies y\:dy=x\:dx$

On integration, we get

$\int y\:dy=\int x\:dx$

$\implies \frac{y^{2}}{2}=\frac{x^{2}}{2}+C$

where C is integral constant

$\implies y^{2}=x^{2}+2C$

which is the required solution

Rule :

$\int x^{n}\:dx=\frac{x^{n+1}}{n+1}+C$

where C is integral constant