ODE
\[ (1-x) x (x+1)^2 y''(x)+2 (3-x) x (x+1) y'(x)-2 (1-x) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0359469 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \frac {c_2 x^2+c_1 x-2 c_2 x \log (x)-c_2}{(x+1)^2}\right \}\right \}\]
Maple ✓
cpu = 0.027 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) ={\frac {-2\,\ln \left ( x \right ) {\it \_C2}\,x+{\it \_C2}\,{x}^{2}+{\it \_C1}\,x-{\it \_C2}}{ \left ( 1+x \right ) ^{2}}} \right \} \] Mathematica raw input
DSolve[-2*(1 - x)*y[x] + 2*(3 - x)*x*(1 + x)*y'[x] + (1 - x)*x*(1 + x)^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x*C[1] - C[2] + x^2*C[2] - 2*x*C[2]*Log[x])/(1 + x)^2}}
Maple raw input
dsolve(x*(1-x)*(1+x)^2*diff(diff(y(x),x),x)+2*x*(1+x)*(3-x)*diff(y(x),x)-2*(1-x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (-2*ln(x)*_C2*x+_C2*x^2+_C1*x-_C2)/(1+x)^2