ODE
\[ x y''(x)+y(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0404792 (sec), leaf count = 39
\[\left \{\left \{y(x)\to \sqrt {x} \left (c_1 J_1\left (2 \sqrt {x}\right )+2 i c_2 Y_1\left (2 \sqrt {x}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) =\sqrt {x} \left ( {{\sl Y}_{1}\left (2\,\sqrt {x}\right )}{\it \_C2}+{{\sl J}_{1}\left (2\,\sqrt {x}\right )}{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[y[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[x]*(BesselJ[1, 2*Sqrt[x]]*C[1] + (2*I)*BesselY[1, 2*Sqrt[x]]*C[2])}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x^(1/2)*(BesselY(1,2*x^(1/2))*_C2+BesselJ(1,2*x^(1/2))*_C1)