\[ \left (-a y(x)-b+4 y(x)^3\right ) \left (f(x) y'(x)+y''(x)\right )+\left (\frac {a}{2}-6 y(x)^2\right ) y'(x)^2=0 \] ✓ Mathematica : cpu = 0.393584 (sec), leaf count = 438
DSolve[(a/2 - 6*y[x]^2)*Derivative[1][y][x]^2 + (-b - a*y[x] + 4*y[x]^3)*(f[x]*Derivative[1][y][x] + Derivative[2][y][x]) == 0,y[x],x]
\[\text {Solve}\left [\frac {2 \sqrt {\frac {y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,1\right ]}{\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,1\right ]}} \sqrt {\frac {y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,2\right ]}{\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,2\right ]}} \left (y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]\right ) F\left (\sin ^{-1}\left (\sqrt {\frac {\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]-y(x)}{\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]-\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,2\right ]}}\right )|\frac {\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,2\right ]-\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]}{\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,1\right ]-\text {Root}\left [4 \text {$\#$1}^3-a \text {$\#$1}-b\& ,3\right ]}\right )}{\sqrt {a y(x)+b-4 y(x)^3} \sqrt {\frac {y(x)-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]}{\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,2\right ]-\text {Root}\left [4 \text {$\#$1}^3-\text {$\#$1} a-b\& ,3\right ]}}}=\int _1^x-\sqrt {2} \exp \left (-\int _1^{K[3]}f(K[1])dK[1]\right ) c_1dK[3]+c_2,y(x)\right ]\] ✓ Maple : cpu = 0.055 (sec), leaf count = 34
dsolve((4*y(x)^3-a*y(x)-b)*(diff(diff(y(x),x),x)+f*diff(y(x),x))-(6*y(x)^2-1/2*a)*diff(y(x),x)^2=0,y(x))
\[c_{1} {\mathrm e}^{-f x}-c_{2}+\int _{}^{y \left (x \right )}\frac {1}{\sqrt {4 \textit {\_a}^{3}-a \textit {\_a} -b}}d \textit {\_a} = 0\]