\[ \left (-a y(x)-b+4 y(x)^3\right ) \left (f(x) y'(x)+y''(x)\right )-\left (6 y(x)^2-\frac {a}{2}\right ) y'(x)^2=0 \] ✓ Mathematica : cpu = 3.29824 (sec), leaf count = 436
\[\text {Solve}\left [\frac {2 \sqrt {\frac {\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,1\right ]-y(x)}{\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,1\right ]-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]}} \sqrt {\frac {\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,2\right ]-y(x)}{\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,2\right ]-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]}} \left (y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]\right ) F\left (\sin ^{-1}\left (\sqrt {\frac {y(x)-\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]}{\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,2\right ]-\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]}}\right )|\frac {\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,2\right ]-\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]}{\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,1\right ]-\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]}\right )}{\sqrt {a y(x)+b-4 y(x)^3} \sqrt {\frac {y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]}{\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,2\right ]-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]}}}=\int _1^x -\sqrt {2} c_1 e^{-\int _1^{K[3]} f(K[1]) \, dK[1]} \, dK[3]+c_2,y(x)\right ]\]
✓ Maple : cpu = 0.046 (sec), leaf count = 34
\[ \left \{ {\it \_C1}\,{{\rm e}^{-fx}}-{\it \_C2}+\int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt {4\,{{\it \_a}}^{3}-a{\it \_a}-b}}}{d{\it \_a}}=0 \right \} \]