ODE
\[ (x+2)^2 y''(x)-(x+2) y'(x)+2 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.170563 (sec), leaf count = 26
\[\{\{y(x)\to (x+2) (c_2 \cos (\log (x+2))+c_1 \sin (\log (x+2)))\}\}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 25
\[[y \left (x \right ) = \textit {\_C1} \left (2+x \right ) \sin \left (\ln \left (2+x \right )\right )+\textit {\_C2} \left (2+x \right ) \cos \left (\ln \left (2+x \right )\right )]\] Mathematica raw input
DSolve[2*y[x] - (2 + x)*y'[x] + (2 + x)^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (2 + x)*(C[2]*Cos[Log[2 + x]] + C[1]*Sin[Log[2 + x]])}}
Maple raw input
dsolve((2+x)^2*diff(diff(y(x),x),x)-(2+x)*diff(y(x),x)+2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(2+x)*sin(ln(2+x))+_C2*(2+x)*cos(ln(2+x))]