\[ \boxed { 2\, \left ( -{x}^{k}+4\,{x}^{3} \right ) \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +y \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{3} \right ) - \left ( k{x}^{k-1}-12\,{x}^{2} \right ) \left ( 3\,{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{2} \right ) +axy \left ( x \right ) +b=0} \]
Mathematica: cpu = 4.994134 (sec), leaf count = 70 \[ \text {DSolve}\left [a x y(x)+b-\left (k x^{k-1}-12 x^2\right ) \left (3 y'(x)+y(x)^2\right )+2 \left (4 x^3-x^k\right ) \left (y''(x)+y(x) y'(x)-y(x)^3\right )=0,y(x),x\right ] \]
Maple: cpu = 3.650 (sec), leaf count = 0 \[ \text {could not solve} \]