Question

Solve:

$\frac{dy}{dx}=\frac{x+2y}{x}$.

Answer 1

Now,

$\frac{dy}{dx}=\frac{x+2y}{x}$

or, $\frac{dy}{dx}-2\frac{y}{x}=1$

or, $\frac{1}{x^2}\frac{dy}{dx}-2\frac{y}{x^3}=\frac{1}{x^2}$

or, $d\left(\frac{y}{x^2}\right)=\frac{1}{x^2}$

or, $\frac{y}{x^2}=-\frac{1}{x}+c$ [ Where $c$ is integrating constant]

or, $y=c{x}^2-x$.