4.30.43 2axy(x)+a(a+1)y(x)+x2y(x)=0

ODE
2axy(x)+a(a+1)y(x)+x2y(x)=0 ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.0216746 (sec), leaf count = 105

{{y(x)x1a2+aa1a2+aa3/2+2a+1a+a+12a+1(c2xaa+11a2+a+c1)}}

Maple
cpu = 0.01 (sec), leaf count = 17

{y(x)=_C1x1+a+_C2xa} Mathematica raw input

DSolve[a*(1 + a)*y[x] - 2*a*x*y'[x] + x^2*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> x^((Sqrt[1 + a] + 2*a*Sqrt[1 + a] - Sqrt[a]*Sqrt[(a + a^2)^(-1)] - a^(
3/2)*Sqrt[(a + a^2)^(-1)])/(2*Sqrt[1 + a]))*(C[1] + x^(Sqrt[a]*Sqrt[1 + a]*Sqrt[
(a + a^2)^(-1)])*C[2])}}

Maple raw input

dsolve(x^2*diff(diff(y(x),x),x)-2*a*x*diff(y(x),x)+a*(1+a)*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*x^(1+a)+_C2*x^a