\[ a y'(x)^2+b x^2 y'(x)+c x y(x)=0 \] ✓ Mathematica : cpu = 1.80238 (sec), leaf count = 308
DSolve[c*x*y[x] + b*x^2*Derivative[1][y][x] + a*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\text {Solve}\left [\frac {-6 b \text {arctanh}\left (\frac {b x \sqrt {b^2 x^4-4 a c x y(x)}}{b^2 x^3-4 a c y(x)}\right )+(6 b+4 c) \text {arctanh}\left (\frac {x^2 (3 b+2 c)}{3 \sqrt {b^2 x^4-4 a c x y(x)}}\right )+(3 b+2 c) \log \left (9 a y(x)+3 b x^3+c x^3\right )}{6 (3 b+c)}+\frac {b \log (6 b y(x)+2 c y(x))}{2 (3 b+c)}=c_1,y(x)\right ],\text {Solve}\left [\frac {6 b \text {arctanh}\left (\frac {b x \sqrt {b^2 x^4-4 a c x y(x)}}{b^2 x^3-4 a c y(x)}\right )-2 (3 b+2 c) \text {arctanh}\left (\frac {x^2 (3 b+2 c)}{3 \sqrt {b^2 x^4-4 a c x y(x)}}\right )+(3 b+2 c) \log \left (9 a y(x)+3 b x^3+c x^3\right )}{6 (3 b+c)}+\frac {b \log (6 b y(x)+2 c y(x))}{2 (3 b+c)}=c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.416 (sec), leaf count = 389
dsolve(a*diff(y(x),x)^2+b*x^2*diff(y(x),x)+c*x*y(x) = 0,y(x))
\[\int _{\textit {\_b}}^{x}\frac {-b \,\textit {\_a}^{2}+\sqrt {\textit {\_a}^{4} b^{2}-4 \textit {\_a} a c y \left (x \right )}}{b \,\textit {\_a}^{3}+6 a y \left (x \right )-\sqrt {\textit {\_a}^{4} b^{2}-4 \textit {\_a} a c y \left (x \right )}\, \textit {\_a}}d \textit {\_a} +\int _{}^{y \left (x \right )}\left (\frac {2 a}{-b \,x^{3}+\sqrt {b^{2} x^{4}-4 \textit {\_f} a c x}\, x -6 \textit {\_f} a}-\left (\int _{\textit {\_b}}^{x}-\frac {6 a \left (\frac {2 a c \textit {\_a} \textit {\_f}}{\sqrt {\textit {\_a}^{4} b^{2}-4 \textit {\_a} \textit {\_f} a c}}-b \,\textit {\_a}^{2}+\sqrt {\textit {\_a}^{4} b^{2}-4 \textit {\_a} \textit {\_f} a c}\right )}{\left (b \,\textit {\_a}^{3}-\sqrt {\textit {\_a}^{4} b^{2}-4 \textit {\_a} \textit {\_f} a c}\, \textit {\_a} +6 \textit {\_f} a \right )^{2}}d \textit {\_a} \right )\right )d \textit {\_f} +c_{1} = 0\]