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 = 0.174698 (sec), leaf count = 38
\[\left \{\left \{y(x)\to c_1 x e^{-i a x}-\frac {i c_2 x e^{i a x}}{2 a}\right \}\right \}\]
Maple ✓
cpu = 0.097 (sec), leaf count = 19
\[[y \left (x \right ) = \textit {\_C1} x \sin \left (a x \right )+\textit {\_C2} x \cos \left (a x \right )]\] 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^(I*a*x) - ((I/2)*E^(I*a*x)*x*C[2])/a}}
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))
Maple raw output
[y(x) = _C1*x*sin(a*x)+_C2*x*cos(a*x)]