\[ \boxed { \left ( a \left ( y \left ( x \right ) \right ) ^{2}+bx+c \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-by \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +d \left ( y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 33.600767 (sec), leaf count = 913 \[ \left \{\text {Solve}\left [\left \{y(x)=\frac {b \text {K$\$$1419264}-\sqrt {-\text {K$\$$1419264}^2 \left (-b^2+4 a \text {K$\$$1419264}^2 x b+4 d x b+4 a c \text {K$\$$1419264}^2+4 c d\right )}}{2 \left (a \text {K$\$$1419264}^2+d\right )},x=\frac {-b^2 c_1^2 d^4-a b^2 \text {K$\$$1419264}^2 c_1^2 d^3+2 b^2 c_1 \log (\text {K$\$$1419264}) d^{5/2}-2 b^2 c_1 \log \left (d+\sqrt {a \text {K$\$$1419264}^2+d} \sqrt {d}\right ) d^{5/2}-4 c d^2+2 b^2 \sqrt {a \text {K$\$$1419264}^2+d} c_1 d^2+2 a b^2 \text {K$\$$1419264}^2 c_1 \log (\text {K$\$$1419264}) d^{3/2}-2 a b^2 \text {K$\$$1419264}^2 c_1 \log \left (d+\sqrt {a \text {K$\$$1419264}^2+d} \sqrt {d}\right ) d^{3/2}-4 a c \text {K$\$$1419264}^2 d-b^2 \log ^2(\text {K$\$$1419264}) d-b^2 \log ^2\left (d+\sqrt {a \text {K$\$$1419264}^2+d} \sqrt {d}\right ) d+2 b^2 \log (\text {K$\$$1419264}) \log \left (d+\sqrt {a \text {K$\$$1419264}^2+d} \sqrt {d}\right ) d-2 b^2 \sqrt {a \text {K$\$$1419264}^2+d} \log (\text {K$\$$1419264}) \sqrt {d}+2 b^2 \sqrt {a \text {K$\$$1419264}^2+d} \log \left (d+\sqrt {a \text {K$\$$1419264}^2+d} \sqrt {d}\right ) \sqrt {d}-a b^2 \text {K$\$$1419264}^2 \log ^2(\text {K$\$$1419264})-a b^2 \text {K$\$$1419264}^2 \log ^2\left (d+\sqrt {a \text {K$\$$1419264}^2+d} \sqrt {d}\right )+2 a b^2 \text {K$\$$1419264}^2 \log (\text {K$\$$1419264}) \log \left (d+\sqrt {a \text {K$\$$1419264}^2+d} \sqrt {d}\right )}{4 b d \left (a \text {K$\$$1419264}^2+d\right )}\right \},\{y(x),\text {K$\$$1419264}\}\right ],\text {Solve}\left [\left \{y(x)=\frac {b \text {K$\$$1419269}+\sqrt {-\text {K$\$$1419269}^2 \left (-b^2+4 a \text {K$\$$1419269}^2 x b+4 d x b+4 a c \text {K$\$$1419269}^2+4 c d\right )}}{2 \left (a \text {K$\$$1419269}^2+d\right )},x=\frac {-b^2 c_1^2 d^4-a b^2 \text {K$\$$1419269}^2 c_1^2 d^3+2 b^2 c_1 \log (\text {K$\$$1419269}) d^{5/2}-2 b^2 c_1 \log \left (d+\sqrt {a \text {K$\$$1419269}^2+d} \sqrt {d}\right ) d^{5/2}-4 c d^2+2 b^2 \sqrt {a \text {K$\$$1419269}^2+d} c_1 d^2+2 a b^2 \text {K$\$$1419269}^2 c_1 \log (\text {K$\$$1419269}) d^{3/2}-2 a b^2 \text {K$\$$1419269}^2 c_1 \log \left (d+\sqrt {a \text {K$\$$1419269}^2+d} \sqrt {d}\right ) d^{3/2}-4 a c \text {K$\$$1419269}^2 d-b^2 \log ^2(\text {K$\$$1419269}) d-b^2 \log ^2\left (d+\sqrt {a \text {K$\$$1419269}^2+d} \sqrt {d}\right ) d+2 b^2 \log (\text {K$\$$1419269}) \log \left (d+\sqrt {a \text {K$\$$1419269}^2+d} \sqrt {d}\right ) d-2 b^2 \sqrt {a \text {K$\$$1419269}^2+d} \log (\text {K$\$$1419269}) \sqrt {d}+2 b^2 \sqrt {a \text {K$\$$1419269}^2+d} \log \left (d+\sqrt {a \text {K$\$$1419269}^2+d} \sqrt {d}\right ) \sqrt {d}-a b^2 \text {K$\$$1419269}^2 \log ^2(\text {K$\$$1419269})-a b^2 \text {K$\$$1419269}^2 \log ^2\left (d+\sqrt {a \text {K$\$$1419269}^2+d} \sqrt {d}\right )+2 a b^2 \text {K$\$$1419269}^2 \log (\text {K$\$$1419269}) \log \left (d+\sqrt {a \text {K$\$$1419269}^2+d} \sqrt {d}\right )}{4 b d \left (a \text {K$\$$1419269}^2+d\right )}\right \},\{y(x),\text {K$\$$1419269}\}\right ]\right \} \]
Maple: cpu = 4.259 (sec), leaf count = 287 \[ \left \{ [x \left ( {\it \_T} \right ) =-{\frac {1}{4\,bd} \left ( \left ( \ln \left ( 2 \right ) \right ) ^{2}\sqrt {{{\it \_T}}^{2}a+d}{ b}^{2}+2\,\ln \left ( 2 \right ) \ln \left ( {\frac {\sqrt {d}\sqrt {{{ \it \_T}}^{2}a+d}+d}{{\it \_T}}} \right ) \sqrt {{{\it \_T}}^{2}a+d}{b} ^{2}+4\,\ln \left ( 2 \right ) \sqrt {d}\sqrt {{{\it \_T}}^{2}a+d}{\it \_C1}\,b+ \left ( \ln \left ( {\frac {1}{{\it \_T}} \left ( \sqrt {d} \sqrt {{{\it \_T}}^{2}a+d}+d \right ) } \right ) \right ) ^{2}\sqrt {{{ \it \_T}}^{2}a+d}{b}^{2}+4\,\ln \left ( {\frac {\sqrt {d}\sqrt {{{\it \_T}}^{2}a+d}+d}{{\it \_T}}} \right ) \sqrt {d}\sqrt {{{\it \_T}}^{2}a+ d}{\it \_C1}\,b+4\,d\sqrt {{{\it \_T}}^{2}a+d}{{\it \_C1}}^{2}-2\,\ln \left ( 2 \right ) \sqrt {d}{b}^{2}-2\,\ln \left ( {\frac {\sqrt {d} \sqrt {{{\it \_T}}^{2}a+d}+d}{{\it \_T}}} \right ) \sqrt {d}{b}^{2}+4\, cd\sqrt {{{\it \_T}}^{2}a+d}-4\,d{\it \_C1}\,b \right ) {\frac {1}{ \sqrt {{{\it \_T}}^{2}a+d}}}},y \left ( {\it \_T} \right ) ={\frac {{ \it \_T}}{2} \left ( b\ln \left ( 2 \right ) +b\ln \left ( {\frac {1}{{ \it \_T}} \left ( \sqrt {d}\sqrt {{{\it \_T}}^{2}a+d}+d \right ) } \right ) +2\,{\it \_C1}\,\sqrt {d} \right ) {\frac {1}{\sqrt {d}}}{ \frac {1}{\sqrt {{{\it \_T}}^{2}a+d}}}}] \right \} \]