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 = 0.0092332 (sec), leaf count = 18
\[\left \{\left \{y(x)\to c_2 \sin (\log (x))+c_1 \cos (\log (x))\right \}\right \}\]
Maple ✓
cpu = 0.006 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( \ln \left ( x \right ) \right ) +{\it \_C2}\,\cos \left ( \ln \left ( x \right ) \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1*sin(ln(x))+_C2*cos(ln(x))