\[ y''(x) \left (-a y(x)-b+4 y(x)^3\right )+\left (\frac {a}{2}-6 y(x)^2\right ) y'(x)^2=0 \] ✓ Mathematica : cpu = 11.7614 (sec), leaf count = 416
DSolve[(a/2 - 6*y[x]^2)*Derivative[1][y][x]^2 + (-b - a*y[x] + 4*y[x]^3)*Derivative[2][y][x] == 0,y[x],x]
\[\text {Solve}\left [\frac {\sqrt {2} \sqrt {\frac {y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,1\right ]}{\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,1\right ]}} \sqrt {\frac {y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,2\right ]}{\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,2\right ]}} \left (y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]\right ) \operatorname {EllipticF}\left (\arcsin \left (\sqrt {\frac {\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]-y(x)}{\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]-\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,2\right ]}}\right ),\frac {\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,2\right ]-\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]}{\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,1\right ]-\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]}\right )}{c_1 \sqrt {a y(x)+b-4 y(x)^3} \sqrt {\frac {y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]}{\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,2\right ]-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]}}}=x+c_2,y(x)\right ]\] ✓ Maple : cpu = 0.035 (sec), leaf count = 31
dsolve((4*y(x)^3-a*y(x)-b)*diff(diff(y(x),x),x)-(6*y(x)^2-1/2*a)*diff(y(x),x)^2=0,y(x))
\[\int _{}^{y \left (x \right )}\frac {1}{\sqrt {4 \textit {\_a}^{3}-\textit {\_a} a -b}}d \textit {\_a} -x c_{1}-c_{2} = 0\]