\[ y'(x)=\frac {(x y(x)+1)^3}{x^5} \] ✓ Mathematica : cpu = 0.212859 (sec), leaf count = 157
DSolve[Derivative[1][y][x] == (1 + x*y[x])^3/x^5,y[x],x]
\[\text {Solve}\left [\frac {\arctan \left (\frac {\frac {2 \left (\frac {3}{x^3}+\frac {3 y(x)}{x^2}\right )}{3 \sqrt [3]{-\frac {1}{x^6}}}-1}{\sqrt {3}}\right )}{\sqrt {3}}+\frac {1}{3} \log \left (\frac {\frac {3}{x^3}+\frac {3 y(x)}{x^2}}{3 \sqrt [3]{-\frac {1}{x^6}}}+1\right )-\frac {1}{6} \log \left (\frac {\left (\frac {3}{x^3}+\frac {3 y(x)}{x^2}\right )^2}{9 \left (-\frac {1}{x^6}\right )^{2/3}}-\frac {\frac {3}{x^3}+\frac {3 y(x)}{x^2}}{3 \sqrt [3]{-\frac {1}{x^6}}}+1\right )=-\left (-\frac {1}{x^6}\right )^{2/3} x^3+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.436 (sec), leaf count = 84
dsolve(diff(y(x),x) = (x*y(x)+1)^3/x^5,y(x))
\[y \left (x \right ) = \frac {\left (3 \tan \left (\operatorname {RootOf}\left (18 x^{3} \left (-\frac {1}{x^{6}}\right )^{\frac {2}{3}}+6 \sqrt {3}\, \textit {\_Z} +\ln \left (\frac {\left (\sqrt {3}+\tan \left (\textit {\_Z} \right )\right )^{6}}{\left (\tan \left (\textit {\_Z} \right )^{2}+1\right )^{3}}\right )-18 c_{1}\right )\right ) x^{3} \left (-\frac {1}{x^{6}}\right )^{\frac {1}{3}}+\sqrt {3}\, \left (x^{3} \left (-\frac {1}{x^{6}}\right )^{\frac {1}{3}}-2\right )\right ) \sqrt {3}}{6 x}\]