\[ y''(x) \left (-a y(x)-b+4 y(x)^3\right )-\left (6 y(x)^2-\frac {a}{2}\right ) y'(x)^2=0 \] ✓ Mathematica : cpu = 3.13136 (sec), leaf count = 415
\[\text {Solve}\left [\frac {2 \sqrt {\frac {y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,1\right ]}{\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,1\right ]}} \sqrt {\frac {y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,2\right ]}{\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,2\right ]}} \left (y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]\right ) F\left (\sin ^{-1}\left (\sqrt {\frac {\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]-y(x)}{\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]-\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,2\right ]}}\right )|\frac {\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,2\right ]-\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]}{\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,1\right ]-\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]}\right )}{c_1 \sqrt {2 a y(x)+2 b-8 y(x)^3} \sqrt {\frac {y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]}{\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,2\right ]-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]}}}=c_2+x,y(x)\right ]\]
✓ Maple : cpu = 0.038 (sec), leaf count = 31
\[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt {4\,{{\it \_a}}^{3}-{\it \_a}\,a-b}}}{d{\it \_a}}-{\it \_C1}\,x-{\it \_C2}=0 \right \} \]