ODE
\[ x^3 y''(x)+2 x y'(x)-y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.23548 (sec), leaf count = 47
\[\left \{\left \{y(x)\to c_2 G_{1,2}^{2,0}\left (-\frac {2}{x}|\begin {array}{c} \frac {1}{2} \\ -1,0 \\\end {array}\right )+c_1 e^{\frac {1}{x}} \left (I_0\left (\frac {1}{x}\right )-I_1\left (\frac {1}{x}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.211 (sec), leaf count = 47
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{\frac {1}{x}} \left (\BesselI \left (0, \frac {1}{x}\right )-\BesselI \left (1, \frac {1}{x}\right )\right )+\textit {\_C2} \,{\mathrm e}^{\frac {1}{x}} \left (-\BesselK \left (0, -\frac {1}{x}\right )+\BesselK \left (1, -\frac {1}{x}\right )\right )\right ]\] Mathematica raw input
DSolve[-y[x] + 2*x*y'[x] + x^3*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^x^(-1)*(BesselI[0, x^(-1)] - BesselI[1, x^(-1)])*C[1] + C[2]*MeijerG[{{}, {1/2}}, {{-1, 0}, {}}, -2/x]}}
Maple raw input
dsolve(x^3*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(1/x)*(BesselI(0,1/x)-BesselI(1,1/x))+_C2*exp(1/x)*(-BesselK(0,-1/x)+BesselK(1,-1/x))]