Find the general solution $x\frac{dy}{dx} - y = \frac{1}{x^2}$
Solution 1:
Divide the entire equation by $x^{2}$.
Then you get :-
$$\frac{1}{x}\frac{dy}{dx}-\frac{y}{x^{2}}=\frac{1}{x^{4}}$$.
So $$\frac{d(\frac{y}{x})}{dx}=\frac{1}{x^{4}}$$.
So $$\frac{y}{x}=\frac{-1}{3x^{3}}+C$$.
Or $$y=\frac{-1}{3x^{2}}+Cx$$