Answer
$\frac{3}{4}x^{2}-\frac{5}{x}+cx^{-2}$
Work Step by Step
Solve by integrating factor, I(x)
I(x)
= $e^{\int\frac{2}{x}dx}$
= $e^{2lnx}$
= $x^{2}$
$$x^{2}y=\int x^{2}(3x-5) dx$$
$$x^{2}y=\int (3x^{3}-5) dx$$
$$x^{2}y=\frac{3}{4}x^{4}-{5}{x}+c$$
$$y=\frac{3}{4}x^{2}-\frac{5}{x}+cx^{-2}$$
