4.34.11 \(x^3 y''(x)+2 x y'(x)-y(x)=0\)

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 = 0.261784 (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 = 0.099 (sec), leaf count = 44

\[ \left \{ y \left ( x \right ) ={{\rm e}^{{x}^{-1}}} \left ( -{\it \_C2}\,{{\sl K}_{1}\left (-{x}^{-1}\right )}+{\it \_C2}\,{{\sl K}_{0}\left (-{x}^{-1}\right )}+{\it \_C1}\, \left ( {{\sl I}_{0}\left ({x}^{-1}\right )}-{{\sl I}_{1}\left ({x}^{-1}\right )} \right ) \right ) \right \} \] 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),'implicit')

Maple raw output

y(x) = exp(1/x)*(-_C2*BesselK(1,-1/x)+_C2*BesselK(0,-1/x)+_C1*(BesselI(0,1/x)-Be
sselI(1,1/x)))