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 = 0.0261937 (sec), leaf count = 17
\[\left \{\left \{y(x)\to x \left (c_2 (x+\log (x))+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) =x \left ( \ln \left ( x \right ) {\it \_C2}+{\it \_C2}\,x+{\it \_C1} \right ) \right \} \] 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*(1+x)*diff(diff(y(x),x),x)-x*(1+2*x)*diff(y(x),x)+(1+2*x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x*(ln(x)*_C2+_C2*x+_C1)