\[ \boxed { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) +a \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+b \left ( y \left ( x \right ) \right ) ^{3}=0} \]
Mathematica: cpu = 1.553697 (sec), leaf count = 290 \[ \left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {2 a+3} \text {$\#$1}^{a+1} \sqrt {\frac {-2 b \text {$\#$1}^{2 a+3}+2 a c_1+3 c_1}{(2 a+3) c_1}} \, _2F_1\left (\frac {1}{2},\frac {a+1}{2 a+3};\frac {a+1}{2 a+3}+1;\frac {2 b \text {$\#$1}^{2 a+3}}{2 a c_1+3 c_1}\right )}{(a+1) \sqrt {-2 b \text {$\#$1}^{2 a+3}+2 a c_1+3 c_1}}\& \right ]\left [c_2+x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {\sqrt {2 a+3} \text {$\#$1}^{a+1} \sqrt {\frac {-2 b \text {$\#$1}^{2 a+3}+2 a c_1+3 c_1}{(2 a+3) c_1}} \, _2F_1\left (\frac {1}{2},\frac {a+1}{2 a+3};\frac {a+1}{2 a+3}+1;\frac {2 b \text {$\#$1}^{2 a+3}}{2 a c_1+3 c_1}\right )}{(a+1) \sqrt {-2 b \text {$\#$1}^{2 a+3}+2 a c_1+3 c_1}}\& \right ]\left [c_2+x\right ]\right \}\right \} \]
Maple: cpu = 1.716 (sec), leaf count = 108 \[ \left \{ \int ^{y \left ( x \right ) }\!{ \left ( 2\,a+3 \right ) {{\it \_a}}^{2\,a}{\frac {1}{\sqrt {- \left ( 2\,a+3 \right ) {{\it \_a}}^{2\, a} \left ( 2\,{{\it \_a}}^{2\,a+3}b-{\it \_C1} \right ) }}}}{d{\it \_a}} -x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{ \left ( 2\,a+3 \right ) {{\it \_a}}^{2\,a}{\frac {1}{\sqrt {- \left ( 2\,a+3 \right ) {{\it \_a} }^{2\,a} \left ( 2\,{{\it \_a}}^{2\,a+3}b-{\it \_C1} \right ) }}}}{d{ \it \_a}}-x-{\it \_C2}=0 \right \} \]