ODE
\[ x^2 y''(x)-2 (x+1) x y'(x)+2 (x+1) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.157708 (sec), leaf count = 21
\[\left \{\left \{y(x)\to x \left (\frac {1}{2} c_2 e^{2 x}+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.069 (sec), leaf count = 15
\[[y \left (x \right ) = \textit {\_C1} x +\textit {\_C2} \,{\mathrm e}^{2 x} x]\] Mathematica raw input
DSolve[2*(1 + x)*y[x] - 2*x*(1 + x)*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*(C[1] + (E^(2*x)*C[2])/2)}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-2*x*(x+1)*diff(y(x),x)+2*(x+1)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x+_C2*exp(2*x)*x]