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 = 0.0412539 (sec), leaf count = 63
\[\left \{\left \{y(x)\to \frac {e^{\frac {1}{2} x \left (a x-2 \sqrt {-a}\right )} \left (c_2 e^{2 \sqrt {-a} x}+2 \sqrt {-a} c_1\right )}{2 \sqrt {-a}}\right \}\right \}\]
Maple ✓
cpu = 0.052 (sec), leaf count = 39
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{\frac {x}{2} \left ( ax+2\,\sqrt {-a} \right ) }}}+{\it \_C2}\,{{\rm e}^{{\frac {x}{2} \left ( ax-2\,\sqrt {-a} \right ) }}} \right \} \] 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^((x*(-2*Sqrt[-a] + a*x))/2)*(2*Sqrt[-a]*C[1] + E^(2*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),'implicit')
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)))