\[ y(x) \left (a^2 x+2 a b\right )-2 (a x+b) y'(x)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.106843 (sec), leaf count = 77
DSolve[(2*a*b + a^2*x)*y[x] - 2*(b + a*x)*Derivative[1][y][x] + x*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{a x} x^{b-\frac {1}{2} \sqrt {(2 b+1)^2}+\frac {1}{2}}+\frac {c_2 e^{a x} x^{b+\frac {1}{2} \sqrt {(2 b+1)^2}+\frac {1}{2}}}{\sqrt {(2 b+1)^2}}\right \}\right \}\] ✓ Maple : cpu = 0.042 (sec), leaf count = 20
dsolve(x*diff(diff(y(x),x),x)-2*(a*x+b)*diff(y(x),x)+(a^2*x+2*a*b)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{a x} \left (x^{2 b +1} c_{2}+c_{1}\right )\]