ODE
\[ (x+1) x^2 y''(x)-(2 x+1) x y'(x)+(2 x+1) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.173241 (sec), leaf count = 17
\[\{\{y(x)\to x (c_2 (x+\log (x))+c_1)\}\}\]
Maple ✓
cpu = 0.055 (sec), leaf count = 15
\[[y \left (x \right ) = \textit {\_C1} x +\textit {\_C2} x \left (x +\ln \left (x \right )\right )]\] Mathematica raw input
DSolve[(1 + 2*x)*y[x] - x*(1 + 2*x)*y'[x] + x^2*(1 + x)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*(C[1] + C[2]*(x + Log[x]))}}
Maple raw input
dsolve(x^2*(x+1)*diff(diff(y(x),x),x)-x*(1+2*x)*diff(y(x),x)+(1+2*x)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x+_C2*x*(x+ln(x))]