ODE
\[ x (x+1) y''(x)+(1-x) y'(x)+y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0340468 (sec), leaf count = 23
\[\left \{\left \{y(x)\to c_1 (x-1)+c_2 ((x-1) \log (x)-4)\right \}\right \}\]
Maple ✓
cpu = 0.047 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) ={\it \_C2}\, \left ( -1+x \right ) \ln \left ( x \right ) -4\,{\it \_C2}+{\it \_C1}\, \left ( -1+x \right ) \right \} \] Mathematica raw input
DSolve[y[x] + (1 - x)*y'[x] + x*(1 + x)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-1 + x)*C[1] + C[2]*(-4 + (-1 + x)*Log[x])}}
Maple raw input
dsolve(x*(1+x)*diff(diff(y(x),x),x)+(1-x)*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C2*(-1+x)*ln(x)-4*_C2+_C1*(-1+x)