4.28.7 \(x y''(x)+y'(x)-y(x)=0\)

ODE
\[ x y''(x)+y'(x)-y(x)=0 \] ODE Classification

[[_Emden, _Fowler]]

Book solution method
TO DO

Mathematica
cpu = 0.147823 (sec), leaf count = 31

\[\left \{\left \{y(x)\to c_1 I_0\left (2 \sqrt {x}\right )+2 c_2 K_0\left (2 \sqrt {x}\right )\right \}\right \}\]

Maple
cpu = 0.009 (sec), leaf count = 23

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl I}_{0}\left (2\,\sqrt {x}\right )}+{\it \_C2}\,{{\sl K}_{0}\left (2\,\sqrt {x}\right )} \right \} \] Mathematica raw input

DSolve[-y[x] + y'[x] + x*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> BesselI[0, 2*Sqrt[x]]*C[1] + 2*BesselK[0, 2*Sqrt[x]]*C[2]}}

Maple raw input

dsolve(x*diff(diff(y(x),x),x)+diff(y(x),x)-y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*BesselI(0,2*x^(1/2))+_C2*BesselK(0,2*x^(1/2))