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 = 0.183841 (sec), leaf count = 23
\[\{\{y(x)\to c_1 (x-1)+c_2 ((x-1) \log (x)-4)\}\}\]
Maple ✓
cpu = 0.06 (sec), leaf count = 20
\[[y \left (x \right ) = \textit {\_C1} \left (x -1\right )+\textit {\_C2} \left (-4+\left (x -1\right ) \ln \left (x \right )\right )]\] 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*(x+1)*diff(diff(y(x),x),x)+(1-x)*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(x-1)+_C2*(-4+(x-1)*ln(x))]