\[ a y'(x)^2+b x^2 y'(x)+c x y(x)=0 \] ✓ Mathematica : cpu = 2.27835 (sec), leaf count = 795
\[\left \{\text {Solve}\left [\int _1^x\left (\frac {(3 b+2 c) K[1]^2}{2 \left (3 b K[1]^3+c K[1]^3+9 a y(x)\right )}+\frac {3 \sqrt {K[1] \left (b^2 K[1]^3-4 a c y(x)\right )}}{2 \left (3 b K[1]^3+c K[1]^3+9 a y(x)\right )}\right )dK[1]+\int _1^{y(x)}\left (\frac {9 \sqrt {x \left (b^2 x^3-4 a c K[2]\right )} a}{2 (3 b+c) x^2 \left (3 b x^3+c x^3+9 a K[2]\right )}+\frac {3 (3 b+2 c) a}{2 (3 b+c) \left (3 b x^3+c x^3+9 a K[2]\right )}-\int _1^x\left (-\frac {9 a (3 b+2 c) K[1]^2}{2 \left (3 b K[1]^3+c K[1]^3+9 a K[2]\right )^2}-\frac {3 a c K[1]}{\left (3 b K[1]^3+c K[1]^3+9 a K[2]\right ) \sqrt {K[1] \left (b^2 K[1]^3-4 a c K[2]\right )}}-\frac {27 a \sqrt {K[1] \left (b^2 K[1]^3-4 a c K[2]\right )}}{2 \left (3 b K[1]^3+c K[1]^3+9 a K[2]\right )^2}\right )dK[1]-\frac {\sqrt {x \left (b^2 x^3-4 a c K[2]\right )}}{2 (3 b+c) x^2 K[2]}+\frac {b}{2 (3 b+c) K[2]}\right )dK[2]=c_1,y(x)\right ],\text {Solve}\left [\int _1^x\left (\frac {(3 b+2 c) K[3]^2}{2 \left (3 b K[3]^3+c K[3]^3+9 a y(x)\right )}-\frac {3 \sqrt {K[3] \left (b^2 K[3]^3-4 a c y(x)\right )}}{2 \left (3 b K[3]^3+c K[3]^3+9 a y(x)\right )}\right )dK[3]+\int _1^{y(x)}\left (-\frac {9 \sqrt {x \left (b^2 x^3-4 a c K[4]\right )} a}{2 (3 b+c) x^2 \left (3 b x^3+c x^3+9 a K[4]\right )}+\frac {3 (3 b+2 c) a}{2 (3 b+c) \left (3 b x^3+c x^3+9 a K[4]\right )}-\int _1^x\left (-\frac {9 a (3 b+2 c) K[3]^2}{2 \left (3 b K[3]^3+c K[3]^3+9 a K[4]\right )^2}+\frac {3 a c K[3]}{\left (3 b K[3]^3+c K[3]^3+9 a K[4]\right ) \sqrt {K[3] \left (b^2 K[3]^3-4 a c K[4]\right )}}+\frac {27 a \sqrt {K[3] \left (b^2 K[3]^3-4 a c K[4]\right )}}{2 \left (3 b K[3]^3+c K[3]^3+9 a K[4]\right )^2}\right )dK[3]+\frac {\sqrt {x \left (b^2 x^3-4 a c K[4]\right )}}{2 (3 b+c) x^2 K[4]}+\frac {b}{2 (3 b+c) K[4]}\right )dK[4]=c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.256 (sec), leaf count = 389
\[\int _{\textit {\_b}}^{x}\frac {-b \,\textit {\_a}^{2}+\sqrt {\textit {\_a}^{4} b^{2}-4 \textit {\_a} a c y \relax (x )}}{b \,\textit {\_a}^{3}+6 a y \relax (x )-\sqrt {\textit {\_a}^{4} b^{2}-4 \textit {\_a} a c y \relax (x )}\, \textit {\_a}}d \textit {\_a} +\int _{}^{y \relax (x )}\left (\frac {2 a}{-b \,x^{3}+\sqrt {b^{2} x^{4}-4 \textit {\_f} a c x}\, x -6 \textit {\_f} a}-\left (\int _{\textit {\_b}}^{x}-\frac {6 a \left (\frac {2 a c \textit {\_a} \textit {\_f}}{\sqrt {\textit {\_a}^{4} b^{2}-4 \textit {\_a} \textit {\_f} a c}}-b \,\textit {\_a}^{2}+\sqrt {\textit {\_a}^{4} b^{2}-4 \textit {\_a} \textit {\_f} a c}\right )}{\left (b \,\textit {\_a}^{3}+6 \textit {\_f} a -\sqrt {\textit {\_a}^{4} b^{2}-4 \textit {\_a} \textit {\_f} a c}\, \textit {\_a} \right )^{2}}d \textit {\_a} \right )\right )d \textit {\_f} +c_{1} = 0\]