ODE
\[ x^2 y''(x)+x y'(x)+y(x)=0 \] ODE Classification
[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.165227 (sec), leaf count = 18
\[\{\{y(x)\to c_1 \cos (\log (x))+c_2 \sin (\log (x))\}\}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 15
\[[y \left (x \right ) = \sin \left (\ln \left (x \right )\right ) \textit {\_C1} +\textit {\_C2} \cos \left (\ln \left (x \right )\right )]\] Mathematica raw input
DSolve[y[x] + x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Cos[Log[x]] + C[2]*Sin[Log[x]]}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = sin(ln(x))*_C1+_C2*cos(ln(x))]