✓ Mathematica : cpu = 0.0587004 (sec), leaf count = 62
DSolve[Derivative[2][y][x] == -1/4*((a - b)*y[x])/((a + x)^2*(b + x)) - ((a + 2*b + 3*x)*Derivative[1][y][x])/(2*(a + x)*(b + x)),y[x],x]
✓ Maple : cpu = 0.066 (sec), leaf count = 27
dsolve(diff(diff(y(x),x),x) = -1/2/(x+a)*(3*x+a+2*b)/(x+b)*diff(y(x),x)-1/4*(a-b)/(x+a)^2/(x+b)*y(x),y(x))