\[ \boxed { \left ( 4\, \left ( y \left ( x \right ) \right ) ^{3}-ay \left ( x \right ) -b \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( 6\, \left ( y \left ( x \right ) \right ) ^{2}-a/2 \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 2.998381 (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 = 0.031 (sec), leaf count = 31 \[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt {4\,{{\it \_a}} ^{3}-a{\it \_a}-b}}}{d{\it \_a}}-{\it \_C1}\,x-{\it \_C2}=0 \right \} \]