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 = 0.0198417 (sec), leaf count = 57
\[\left \{\left \{y(x)\to c_1 x^a e^{-\sqrt {-b^2} x}+\frac {c_2 x^a e^{\sqrt {-b^2} x}}{2 \sqrt {-b^2}}\right \}\right \}\]
Maple ✓
cpu = 0.041 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) ={x}^{a} \left ( \cos \left ( bx \right ) {\it \_C2}+\sin \left ( bx \right ) {\it \_C1} \right ) \right \} \] 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^(Sqrt[-b^2]*x) + (E^(Sqrt[-b^2]*x)*x^a*C[2])/(2*Sqrt[-b^2])}}
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),'implicit')
Maple raw output
y(x) = x^a*(cos(b*x)*_C2+sin(b*x)*_C1)