\[ \boxed { xy \left ( x \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -x \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+y \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +x \left ( d+a \left ( y \left ( x \right ) \right ) ^{4} \right ) +y \left ( x \right ) \left ( c+b \left ( y \left ( x \right ) \right ) ^{2} \right ) =0} \]
Mathematica: cpu = 1.733720 (sec), leaf count = 52 \[ \text {DSolve}\left [x \left (a y(x)^4+d\right )+y(x) \left (b y(x)^2+c\right )+x y(x) y''(x)-x y'(x)^2+y(x) y'(x)=0,y(x),x\right ] \]
Maple: cpu = 2.184 (sec), leaf count = 0 \[ \text {could not solve} \]