\[ a y(x)^3+b y(x)^2+c y(x)+d+y''(x)=0 \] ✓ Mathematica : cpu = 1.51541 (sec), leaf count = 1017
\[\text {Solve}\left [\frac {4 F\left (\sin ^{-1}\left (\sqrt {\frac {\left (\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,2\right ]-\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,4\right ]\right ) \left (y(x)-\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,1\right ]\right )}{\left (\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,1\right ]-\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,4\right ]\right ) \left (y(x)-\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,2\right ]\right )}}\right )|\frac {\left (\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,2\right ]-\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,3\right ]\right ) \left (\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,1\right ]-\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,4\right ]\right )}{\left (\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,1\right ]-\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,3\right ]\right ) \left (\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,2\right ]-\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,4\right ]\right )}\right ){}^2 \left (\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,1\right ]-\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,2\right ]\right ){}^2 \left (y(x)-\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,1\right ]\right ) \left (y(x)-\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,2\right ]\right ) \left (y(x)-\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,3\right ]\right ) \left (y(x)-\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,4\right ]\right )}{\left (\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,2\right ]-\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,1\right ]\right ){}^2 \left (\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,1\right ]-\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,3\right ]\right ) \left (\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,2\right ]-\text {Root}\left [3 a \text {$\#$1}^4+4 b \text {$\#$1}^3+6 c \text {$\#$1}^2+12 d \text {$\#$1}-6 c_1\& ,4\right ]\right ) \left (-\frac {1}{2} a y(x)^4-\frac {2}{3} b y(x)^3-c y(x)^2-2 d y(x)+c_1\right )}=(x+c_2){}^2,y(x)\right ]\] ✓ Maple : cpu = 0.167 (sec), leaf count = 89
\[ \left \{ \int ^{y \left ( x \right ) }\!-6\,{\frac {1}{\sqrt {-18\,{{\it \_a}}^{4}a-24\,b{{\it \_a}}^{3}-36\,{{\it \_a}}^{2}c-72\,{\it \_a}\,d+36\,{\it \_C1}}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!6\,{\frac {1}{\sqrt {-18\,{{\it \_a}}^{4}a-24\,b{{\it \_a}}^{3}-36\,{{\it \_a}}^{2}c-72\,{\it \_a}\,d+36\,{\it \_C1}}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]