4.34.14 \(x^3 y''(x)+3 x^2 y'(x)+x y(x)=0\)

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