ODE
\[ x y''(x)+y'(x)-y(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.169251 (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 = 0.01 (sec), leaf count = 23
\[\left [y \left (x \right ) = \textit {\_C1} \BesselI \left (0, 2 \sqrt {x}\right )+\textit {\_C2} \BesselK \left (0, 2 \sqrt {x}\right )\right ]\] 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))
Maple raw output
[y(x) = _C1*BesselI(0,2*x^(1/2))+_C2*BesselK(0,2*x^(1/2))]