\[ x^4 y''(x)-x^2 y'(x) \left (y'(x)+x\right )+4 y(x)^2=0 \] ✓ Mathematica : cpu = 0.516153 (sec), leaf count = 189
\[\text {Solve}\left [\int _1^{y(x)}\frac {1}{-e^{\frac {K[1]}{x^2}} c_1 x^2+2 x^2+4 K[1]}dK[1]-\int _1^x\left (\frac {K[2] \left (e^{\frac {y(x)}{K[2]^2}} c_1+2 \left (-\frac {y(x)}{K[2]^2}-1\right )\right )}{-e^{\frac {y(x)}{K[2]^2}} c_1 K[2]^2+2 K[2]^2+4 y(x)}+\int _1^{y(x)}-\frac {\frac {2 e^{\frac {K[1]}{K[2]^2}} c_1 K[1]}{K[2]}-2 e^{\frac {K[1]}{K[2]^2}} c_1 K[2]+4 K[2]}{\left (-e^{\frac {K[1]}{K[2]^2}} c_1 K[2]^2+2 K[2]^2+4 K[1]\right ){}^2}dK[1]\right )dK[2]=c_2,y(x)\right ]\] ✓ Maple : cpu = 0.926 (sec), leaf count = 32
\[y \relax (x ) = \RootOf \left (-\ln \relax (x )+c_{2}-\left (\int _{}^{\textit {\_Z}}\frac {1}{{\mathrm e}^{\textit {\_f}} c_{1}+4 \textit {\_f} +2}d \textit {\_f} \right )\right ) x^{2}\]