\[ \boxed { \left ( 4\, \left ( y \left ( x \right ) \right ) ^{3}-ay \left ( x \right ) -b \right ) \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +f{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) - \left ( 6\, \left ( y \left ( x \right ) \right ) ^{2}-a/2 \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 1.882239 (sec), leaf count = 436 \[ \text {Solve}\left [\frac {2 \sqrt {\frac {y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,1\right ]}{\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,1\right ]}} \sqrt {\frac {y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,2\right ]}{\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,2\right ]}} \left (y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]\right ) F\left (\sin ^{-1}\left (\sqrt {\frac {\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]-y(x)}{\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]-\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,2\right ]}}\right )|\frac {\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,2\right ]-\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]}{\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,1\right ]-\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]}\right )}{\sqrt {a y(x)+b-4 y(x)^3} \sqrt {\frac {y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]}{\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,2\right ]-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]}}}=\int _1^x -\sqrt {2} c_1 e^{-\int _1^{K[3]} f(K[1]) \, dK[1]} \, dK[3]+c_2,y(x)\right ] \]
Maple: cpu = 0.031 (sec), leaf count = 34 \[ \left \{ {\it \_C1}\,{{\rm e}^{-fx}}-{\it \_C2}+\int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt {4\,{{\it \_a}}^{3}-a{\it \_a}-b}}}{d{ \it \_a}}=0 \right \} \]