First-Order Linear Equations I have the equation,  
$$\frac{dy}{dx} - \frac{2y}{x} = x^2$$
and I have tried solving it using $e^{G(x)}$ but I get the answer $y(x) = x^4$ which isn't correct. I got the integration of $g(x)$ to be $-2ln|x| + C$ which seems to be right but implementing it in the equation didn´t work for me. 
I got
$$\frac{dy}{dx} \frac{1}{x^2} - \frac{2}{x} \frac{1}{x^2}  y = \frac{1}{x^2}  x^2$$
and then 
$$\frac{dy}{dx}\bigg(\frac{1}{x^2} y(x)\bigg) = x^2$$
An ideas?

Here is your mistake:
$$\frac{dy}{dx}\cdot \frac{1}{x^2} - \frac{2}{x} \cdot \frac{1}{x^2} \cdot y = \frac{1}{x^2} \cdot x^2 $$
This leads to:
$$\frac{d}{dx}\left(\frac{1}{x^2} \cdot y(x)\right) = \color{red}{1}$$
Can you continue from here?
