ODE
\[ a x^2 y(x)+x y''(x)+2 y'(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.16608 (sec), leaf count = 36
\[\left \{\left \{y(x)\to \frac {c_1 \text {Ai}\left (\sqrt [3]{-a} x\right )+c_2 \text {Bi}\left (\sqrt [3]{-a} x\right )}{x}\right \}\right \}\]
Maple ✓
cpu = 0.231 (sec), leaf count = 35
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \BesselJ \left (\frac {1}{3}, \frac {2 \sqrt {a}\, x^{\frac {3}{2}}}{3}\right )}{\sqrt {x}}+\frac {\textit {\_C2} \BesselY \left (\frac {1}{3}, \frac {2 \sqrt {a}\, x^{\frac {3}{2}}}{3}\right )}{\sqrt {x}}\right ]\] Mathematica raw input
DSolve[a*x^2*y[x] + 2*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (AiryAi[(-a)^(1/3)*x]*C[1] + AiryBi[(-a)^(1/3)*x]*C[2])/x}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+2*diff(y(x),x)+a*x^2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1/x^(1/2)*BesselJ(1/3,2/3*a^(1/2)*x^(3/2))+_C2/x^(1/2)*BesselY(1/3,2/3*a^(1/2)*x^(3/2))]