\[ x^k \left (-h\left (x^k y(x),k y(x)+x y'(x)\right )\right )+(a+1) x y'(x)+x^2 y''(x)=0 \] ✗ Mathematica : cpu = 3.5192 (sec), leaf count = 0 , could not solve
DSolve[-(x^k*h[x^k*y[x], k*y[x] + x*Derivative[1][y][x]]) + (1 + a)*x*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , could not solve
dsolve(x^2*diff(diff(y(x),x),x)+(a+1)*x*diff(y(x),x)-x^k*h(x^k*y(x),x*diff(y(x),x)+k*y(x))=0,y(x))