ODE
\[ a^2 x^2 y(x)-2 a x y'(x)+y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.185911 (sec), leaf count = 63
\[\left \{\left \{y(x)\to \frac {e^{\frac {a x^2}{2}-i \sqrt {a} x} \left (2 \sqrt {a} c_1-i c_2 e^{2 i \sqrt {a} x}\right )}{2 \sqrt {a}}\right \}\right \}\]
Maple ✓
cpu = 0.116 (sec), leaf count = 39
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{\frac {x \left (a x +2 \sqrt {-a}\right )}{2}}+\textit {\_C2} \,{\mathrm e}^{\frac {x \left (a x -2 \sqrt {-a}\right )}{2}}\right ]\] Mathematica raw input
DSolve[a^2*x^2*y[x] - 2*a*x*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (E^((-I)*Sqrt[a]*x + (a*x^2)/2)*(2*Sqrt[a]*C[1] - I*E^((2*I)*Sqrt[a]*x)*C[2]))/(2*Sqrt[a])}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-2*a*x*diff(y(x),x)+a^2*x^2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(1/2*x*(a*x+2*(-a)^(1/2)))+_C2*exp(1/2*x*(a*x-2*(-a)^(1/2)))]