ODE
\[ \left (x^3+1\right ) y'''(x)+9 x^2 y''(x)+18 x y'(x)+6 y(x)=0 \] ODE Classification
[[_3rd_order, _fully, _exact, _linear]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0209876 (sec), leaf count = 31
\[\left \{\left \{y(x)\to \frac {c_3 x^2+2 c_2 x+2 c_1}{2 x^3+2}\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{x}^{2}+{\it \_C2}\,x+{\it \_C3}}{ \left ( 1+x \right ) \left ( {x}^{2}-x+1 \right ) }} \right \} \] Mathematica raw input
DSolve[6*y[x] + 18*x*y'[x] + 9*x^2*y''[x] + (1 + x^3)*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (2*C[1] + 2*x*C[2] + x^2*C[3])/(2 + 2*x^3)}}
Maple raw input
dsolve((x^3+1)*diff(diff(diff(y(x),x),x),x)+9*x^2*diff(diff(y(x),x),x)+18*x*diff(y(x),x)+6*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C1*x^2+_C2*x+_C3)/(1+x)/(x^2-x+1)