ODE
\[ x^3 y''(x)+3 x^2 y'(x)+x y(x)=0 \] ODE Classification
[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.012563 (sec), leaf count = 17
\[\left \{\left \{y(x)\to \frac {c_2 \log (x)+c_1}{x}\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 14
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}\,\ln \left ( x \right ) +{\it \_C1}}{x}} \right \} \] Mathematica raw input
DSolve[x*y[x] + 3*x^2*y'[x] + x^3*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + C[2]*Log[x])/x}}
Maple raw input
dsolve(x^3*diff(diff(y(x),x),x)+3*x^2*diff(y(x),x)+x*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C2*ln(x)+_C1)/x