Solve differential equation, $x'=x^2-2t^{-2}$ Solve differential equation:
$x'=x^2- \frac{2}{t^2}$
Maybe is it sth connected with homogeneous equation?
I have no idea how to solve it.

$$(tx)'=tx'+x=tx^2-\frac{2}{t}+x=\frac{(tx-1)(tx+2)}{t}$$
$$\Rightarrow\frac{(tx)'}{tx-1}-\frac{(tx)'}{tx+2}=\frac{3}{t}$$
$$\Rightarrow\ln|\frac{tx-1}{tx+2}|=3\ln|t|+\ln|C|$$
$$\Rightarrow x=\frac{1+2Ct^3}{t(1-Ct^3)}$$
