ODE
\[ x^2 y''(x)+\left (x^2+6\right ) y(x)+4 x y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00869498 (sec), leaf count = 44
\[\left \{\left \{y(x)\to \frac {c_1 J_{\frac {i \sqrt {15}}{2}}(x)+c_2 Y_{\frac {i \sqrt {15}}{2}}(x)}{x^{3/2}}\right \}\right \}\]
Maple ✓
cpu = 0.059 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) ={({\it \_C1}\,{{\sl J}_{{\frac {i}{2}}\sqrt {15}}\left (x\right )}+{\it \_C2}\,{{\sl Y}_{{\frac {i}{2}}\sqrt {15}}\left (x\right )}){x}^{-{\frac {3}{2}}}} \right \} \] Mathematica raw input
DSolve[(6 + x^2)*y[x] + 4*x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (BesselJ[(I/2)*Sqrt[15], x]*C[1] + BesselY[(I/2)*Sqrt[15], x]*C[2])/x^(3/2)}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)+(x^2+6)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C1*BesselJ(1/2*I*15^(1/2),x)+_C2*BesselY(1/2*I*15^(1/2),x))/x^(3/2)