ODE
\[ x^4 y''(x)+\left (x^2+1\right ) x y'(x)+y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.262307 (sec), leaf count = 73
\[\left \{\left \{y(x)\to c_2 G_{1,2}^{2,0}\left (-\frac {1}{2 x^2}|\begin {array}{c} \frac {3}{2} \\ 0,0 \\\end {array}\right )+\frac {c_1 e^{\frac {1}{4 x^2}} \left (\left (2 x^2-1\right ) I_0\left (\frac {1}{4 x^2}\right )+I_1\left (\frac {1}{4 x^2}\right )\right )}{2 x^2}\right \}\right \}\]
Maple ✓
cpu = 0.386 (sec), leaf count = 73
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \,{\mathrm e}^{\frac {1}{4 x^{2}}} \left (\left (2 x^{2}-1\right ) \BesselI \left (0, \frac {1}{4 x^{2}}\right )+\BesselI \left (1, \frac {1}{4 x^{2}}\right )\right )}{x^{2}}+\frac {\textit {\_C2} \,{\mathrm e}^{\frac {1}{4 x^{2}}} \left (\left (2 x^{2}-1\right ) \BesselK \left (0, -\frac {1}{4 x^{2}}\right )+\BesselK \left (1, -\frac {1}{4 x^{2}}\right )\right )}{x^{2}}\right ]\] Mathematica raw input
DSolve[y[x] + x*(1 + x^2)*y'[x] + x^4*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (E^(1/(4*x^2))*((-1 + 2*x^2)*BesselI[0, 1/(4*x^2)] + BesselI[1, 1/(4*x^2)])*C[1])/(2*x^2) + C[2]*MeijerG[{{}, {3/2}}, {{0, 0}, {}}, -1/2*1/x^2]}}
Maple raw input
dsolve(x^4*diff(diff(y(x),x),x)+x*(x^2+1)*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = _C1/x^2*exp(1/4/x^2)*((2*x^2-1)*BesselI(0,1/4/x^2)+BesselI(1,1/4/x^2))+_C2/x^2*exp(1/4/x^2)*((2*x^2-1)*BesselK(0,-1/4/x^2)+BesselK(1,-1/4/x^2))]