\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( a+1 \right ) x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -{x}^{k}h \left ( {x}^{k}y \left ( x \right ) ,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ky \left ( x \right ) \right ) =0} \]
Mathematica: cpu = 3.448438 (sec), leaf count = 47 \[ \text {DSolve}\left [x^k \left (-h\left (x^k y(x),k y(x)+x y'(x)\right )\right )+(a+1) x y'(x)+x^2 y''(x)=0,y(x),x\right ] \]
Maple: cpu = 1.638 (sec), leaf count = 0 \[ \text {could not solve} \]