ODE
\[ y(x) \left (a (a+1)+b^2 x^2\right )-2 a x y'(x)+x^2 y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.175787 (sec), leaf count = 42
\[\left \{\left \{y(x)\to c_1 x^a e^{-i b x}-\frac {i c_2 x^a e^{i b x}}{2 b}\right \}\right \}\]
Maple ✓
cpu = 0.132 (sec), leaf count = 23
\[[y \left (x \right ) = \textit {\_C1} \,x^{a} \sin \left (b x \right )+\textit {\_C2} \,x^{a} \cos \left (b x \right )]\] Mathematica raw input
DSolve[(a*(1 + a) + b^2*x^2)*y[x] - 2*a*x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x^a*C[1])/E^(I*b*x) - ((I/2)*E^(I*b*x)*x^a*C[2])/b}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-2*a*x*diff(y(x),x)+(a*(1+a)+b^2*x^2)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^a*sin(b*x)+_C2*x^a*cos(b*x)]