ODE
\[ (1-x) x^2 y''(x)+2 (2-x) x y'(x)+2 (x+1) y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.512954 (sec), leaf count = 29
\[\left \{\left \{y(x)\to \frac {c_2 x \left (x^2-3 x+3\right )+3 c_1}{3 x^2}\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}+{\it \_C2}\, \left ( -1+x \right ) ^{3}}{{x}^{2}}} \right \} \] Mathematica raw input
DSolve[2*(1 + x)*y[x] + 2*(2 - x)*x*y'[x] + (1 - x)*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (3*C[1] + x*(3 - 3*x + x^2)*C[2])/(3*x^2)}}
Maple raw input
dsolve(x^2*(1-x)*diff(diff(y(x),x),x)+2*x*(2-x)*diff(y(x),x)+2*(1+x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C1+_C2*(-1+x)^3)/x^2