ODE
\[ x^4 y''''(x)+6 x^3 y'''(x)+9 x^2 y''(x)+3 x y'(x)+y(x)=0 \] ODE Classification
[[_high_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0123044 (sec), leaf count = 30
\[\left \{\left \{y(x)\to \left (c_4 \log (x)+c_3\right ) \sin (\log (x))+\left (c_2 \log (x)+c_1\right ) \cos (\log (x))\right \}\right \}\]
Maple ✓
cpu = 0.005 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) = \left ( {\it \_C4}\,\ln \left ( x \right ) +{\it \_C2} \right ) \cos \left ( \ln \left ( x \right ) \right ) +\sin \left ( \ln \left ( x \right ) \right ) \left ( {\it \_C3}\,\ln \left ( x \right ) +{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[y[x] + 3*x*y'[x] + 9*x^2*y''[x] + 6*x^3*y'''[x] + x^4*y''''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> Cos[Log[x]]*(C[1] + C[2]*Log[x]) + (C[3] + C[4]*Log[x])*Sin[Log[x]]}}
Maple raw input
dsolve(x^4*diff(diff(diff(diff(y(x),x),x),x),x)+6*x^3*diff(diff(diff(y(x),x),x),x)+9*x^2*diff(diff(y(x),x),x)+3*x*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C4*ln(x)+_C2)*cos(ln(x))+sin(ln(x))*(_C3*ln(x)+_C1)