ODE
\[ (x+2)^2 y'''(x)+(x+2) y''(x)+y'(x)=0 \] ODE Classification
[[_3rd_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.183351 (sec), leaf count = 40
\[\left \{\left \{y(x)\to \frac {1}{2} (x+2) ((c_1-c_2) \cos (\log (x+2))+(c_1+c_2) \sin (\log (x+2)))+c_3\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 26
\[[y \left (x \right ) = \textit {\_C1} +\textit {\_C2} \left (2+x \right ) \sin \left (\ln \left (2+x \right )\right )+\textit {\_C3} \left (2+x \right ) \cos \left (\ln \left (2+x \right )\right )]\] Mathematica raw input
DSolve[y'[x] + (2 + x)*y''[x] + (2 + x)^2*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[3] + ((2 + x)*((C[1] - C[2])*Cos[Log[2 + x]] + (C[1] + C[2])*Sin[Log[2 + x]]))/2}}
Maple raw input
dsolve((2+x)^2*diff(diff(diff(y(x),x),x),x)+(2+x)*diff(diff(y(x),x),x)+diff(y(x),x) = 0, y(x))
Maple raw output
[y(x) = _C1+_C2*(2+x)*sin(ln(2+x))+_C3*(2+x)*cos(ln(2+x))]