ODE
\[ -(a-(2-a) x) y'(x)-a y(x)+x (x+1) y''(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.142953 (sec), leaf count = 67
\[\left \{\left \{y(x)\to \frac {x^{\frac {1}{2} \left (a-\sqrt {(a+1)^2}+1\right )} \left (c_2 x^{\sqrt {(a+1)^2}}+\sqrt {(a+1)^2} c_1\right )}{\sqrt {(a+1)^2} (x+1)}\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{a}x{\it \_C2}+{\it \_C1}}{1+x}} \right \} \] Mathematica raw input
DSolve[-(a*y[x]) - (a - (2 - a)*x)*y'[x] + x*(1 + x)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x^((1 + a - Sqrt[(1 + a)^2])/2)*(Sqrt[(1 + a)^2]*C[1] + x^Sqrt[(1 + a)^2]*C[2]))/(Sqrt[(1 + a)^2]*(1 + x))}}
Maple raw input
dsolve(x*(1+x)*diff(diff(y(x),x),x)-(a-(2-a)*x)*diff(y(x),x)-a*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (x^a*x*_C2+_C1)/(1+x)