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 = 0.16169 (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 = 0.155 (sec), leaf count = 60
\[\left [y \left (x \right ) = \frac {x^{2} \textit {\_C1}}{\left (x +1\right ) \left (x^{2}-x +1\right )}+\frac {x \textit {\_C2}}{\left (x +1\right ) \left (x^{2}-x +1\right )}+\frac {\textit {\_C3}}{\left (x +1\right ) \left (x^{2}-x +1\right )}\right ]\] 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))
Maple raw output
[y(x) = x^2/(x+1)/(x^2-x+1)*_C1+x/(x+1)/(x^2-x+1)*_C2+1/(x+1)/(x^2-x+1)*_C3]