ODE
\[ x^2 y''(x)-(x+2) x y'(x)+(x+2) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0112814 (sec), leaf count = 16
\[\left \{\left \{y(x)\to x \left (c_2 e^x+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.045 (sec), leaf count = 12
\[ \left \{ y \left ( x \right ) =x \left ( {\it \_C1}+{\it \_C2}\,{{\rm e}^{x}} \right ) \right \} \] Mathematica raw input
DSolve[(2 + x)*y[x] - x*(2 + x)*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*(C[1] + E^x*C[2])}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-x*(2+x)*diff(y(x),x)+(2+x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x*(_C1+_C2*exp(x))