\[ y'(x)^2 \left (a y(x)^2+b x+c\right )-b y(x) y'(x)+d y(x)^2=0 \] ✓ Mathematica : cpu = 18.5797 (sec), leaf count = 975
\[\left \{\text {Solve}\left [\left \{y(x)=\frac {b K[1]-\sqrt {-K[1]^2 \left (-b^2+4 a x K[1]^2 b+4 d x b+4 a c K[1]^2+4 c d\right )}}{2 \left (a K[1]^2+d\right )},x=\frac {-b^2 c_1{}^2 d^4-a b^2 c_1{}^2 K[1]^2 d^3+2 b^2 c_1 \log (K[1]) d^{5/2}-2 b^2 c_1 \log \left (d+\sqrt {a K[1]^2+d} \sqrt {d}\right ) d^{5/2}-4 c d^2+2 b^2 c_1 \sqrt {a K[1]^2+d} d^2+2 a b^2 c_1 K[1]^2 \log (K[1]) d^{3/2}-2 a b^2 c_1 K[1]^2 \log \left (d+\sqrt {a K[1]^2+d} \sqrt {d}\right ) d^{3/2}-4 a c K[1]^2 d-b^2 \log ^2(K[1]) d-b^2 \log ^2\left (d+\sqrt {a K[1]^2+d} \sqrt {d}\right ) d+2 b^2 \log (K[1]) \log \left (d+\sqrt {a K[1]^2+d} \sqrt {d}\right ) d-2 b^2 \sqrt {a K[1]^2+d} \log (K[1]) \sqrt {d}+2 b^2 \sqrt {a K[1]^2+d} \log \left (d+\sqrt {a K[1]^2+d} \sqrt {d}\right ) \sqrt {d}-a b^2 K[1]^2 \log ^2(K[1])-a b^2 K[1]^2 \log ^2\left (d+\sqrt {a K[1]^2+d} \sqrt {d}\right )+2 a b^2 K[1]^2 \log (K[1]) \log \left (d+\sqrt {a K[1]^2+d} \sqrt {d}\right )}{4 b d \left (a K[1]^2+d\right )}\right \},\{y(x),K[1]\}\right ],\text {Solve}\left [\left \{y(x)=\frac {b K[2]+\sqrt {-K[2]^2 \left (-b^2+4 a x K[2]^2 b+4 d x b+4 a c K[2]^2+4 c d\right )}}{2 \left (a K[2]^2+d\right )},x=\frac {-b^2 c_1{}^2 d^4-a b^2 c_1{}^2 K[2]^2 d^3+2 b^2 c_1 \log (K[2]) d^{5/2}-2 b^2 c_1 \log \left (d+\sqrt {a K[2]^2+d} \sqrt {d}\right ) d^{5/2}-4 c d^2+2 b^2 c_1 \sqrt {a K[2]^2+d} d^2+2 a b^2 c_1 K[2]^2 \log (K[2]) d^{3/2}-2 a b^2 c_1 K[2]^2 \log \left (d+\sqrt {a K[2]^2+d} \sqrt {d}\right ) d^{3/2}-4 a c K[2]^2 d-b^2 \log ^2(K[2]) d-b^2 \log ^2\left (d+\sqrt {a K[2]^2+d} \sqrt {d}\right ) d+2 b^2 \log (K[2]) \log \left (d+\sqrt {a K[2]^2+d} \sqrt {d}\right ) d-2 b^2 \sqrt {a K[2]^2+d} \log (K[2]) \sqrt {d}+2 b^2 \sqrt {a K[2]^2+d} \log \left (d+\sqrt {a K[2]^2+d} \sqrt {d}\right ) \sqrt {d}-a b^2 K[2]^2 \log ^2(K[2])-a b^2 K[2]^2 \log ^2\left (d+\sqrt {a K[2]^2+d} \sqrt {d}\right )+2 a b^2 K[2]^2 \log (K[2]) \log \left (d+\sqrt {a K[2]^2+d} \sqrt {d}\right )}{4 b d \left (a K[2]^2+d\right )}\right \},\{y(x),K[2]\}\right ]\right \}\] ✓ Maple : cpu = 4.926 (sec), leaf count = 215
\[\left [x \left (\textit {\_T} \right ) = -\frac {\sqrt {\textit {\_T}^{2} a +d}\, \ln \left (\frac {\sqrt {d}\, \sqrt {\textit {\_T}^{2} a +d}+d}{\textit {\_T}}\right )^{2} b^{2}+\left (\left (2 \ln \relax (2) b^{2}+4 \sqrt {d}\, c_{1} b \right ) \sqrt {\textit {\_T}^{2} a +d}-2 \sqrt {d}\, b^{2}\right ) \ln \left (\frac {\sqrt {d}\, \sqrt {\textit {\_T}^{2} a +d}+d}{\textit {\_T}}\right )+\left (4 \sqrt {d}\, \ln \relax (2) c_{1} b +\ln \relax (2)^{2} b^{2}+4 d \left (c_{1}^{2}+c \right )\right ) \sqrt {\textit {\_T}^{2} a +d}-2 \sqrt {d}\, \ln \relax (2) b^{2}-4 d c_{1} b}{4 \sqrt {\textit {\_T}^{2} a +d}\, b d}, y \left (\textit {\_T} \right ) = \frac {\left (2 c_{1} \sqrt {d}+b \ln \left (\frac {\sqrt {d}\, \sqrt {\textit {\_T}^{2} a +d}+d}{\textit {\_T}}\right )+b \ln \relax (2)\right ) \textit {\_T}}{2 \sqrt {d}\, \sqrt {\textit {\_T}^{2} a +d}}\right ]\]