ODE
\[ a x y(x)+x y''(x)+2 y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.171127 (sec), leaf count = 52
\[\left \{\left \{y(x)\to \frac {2 c_1 e^{-i \sqrt {a} x}-\frac {i c_2 e^{i \sqrt {a} x}}{\sqrt {a}}}{2 x}\right \}\right \}\]
Maple ✓
cpu = 0.099 (sec), leaf count = 31
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \sinh \left (x \sqrt {-a}\right )}{x}+\frac {\textit {\_C2} \cosh \left (x \sqrt {-a}\right )}{x}\right ]\] Mathematica raw input
DSolve[a*x*y[x] + 2*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((2*C[1])/E^(I*Sqrt[a]*x) - (I*E^(I*Sqrt[a]*x)*C[2])/Sqrt[a])/(2*x)}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+2*diff(y(x),x)+a*x*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1/x*sinh(x*(-a)^(1/2))+_C2/x*cosh(x*(-a)^(1/2))]