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 = 0.0228534 (sec), leaf count = 26
\[\left \{\left \{y(x)\to (x+2) \left (c_1 \sin (\log (x+2))+c_2 \cos (\log (x+2))\right )\right \}\right \}\]
Maple ✓
cpu = 0.006 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) = \left ( 2+x \right ) \left ( {\it \_C1}\,\sin \left ( \ln \left ( 2+x \right ) \right ) +{\it \_C2}\,\cos \left ( \ln \left ( 2+x \right ) \right ) \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = (2+x)*(_C1*sin(ln(2+x))+_C2*cos(ln(2+x)))