ODE
\[ \left (a^2 x^2+2\right ) y(x)+x^2 y''(x)-2 x y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0138308 (sec), leaf count = 53
\[\left \{\left \{y(x)\to c_1 x e^{-\sqrt {-a^2} x}+\frac {c_2 x e^{\sqrt {-a^2} x}}{2 \sqrt {-a^2}}\right \}\right \}\]
Maple ✓
cpu = 0.035 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) =x \left ( \cos \left ( ax \right ) {\it \_C2}+\sin \left ( ax \right ) {\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[(2 + a^2*x^2)*y[x] - 2*x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x*C[1])/E^(Sqrt[-a^2]*x) + (E^(Sqrt[-a^2]*x)*x*C[2])/(2*Sqrt[-a^2])}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+(a^2*x^2+2)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x*(cos(a*x)*_C2+sin(a*x)*_C1)