ODE
\[ -a y'(x)+(1-x) x y''(x)+2 y(x)=0 \] ODE Classification
[[_2nd_order, _exact, _linear, _homogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.190273 (sec), leaf count = 87
\[\left \{\left \{y(x)\to \frac {\left (a^2+a (2 x-1)+2 (x-1) x\right ) \left (\frac {c_2 x^{a+1} (1-x)^{1-a}}{(a-1) a (a+1) \left (a^2+a (2 x-1)+2 (x-1) x\right )}+c_1\right )}{a^2+3 a+4}\right \}\right \}\]
Maple ✓
cpu = 0.025 (sec), leaf count = 42
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {a}^{2}+a \left ( -1+2\,x \right ) +2\,{x}^{2}-2\,x \right ) +{\frac {{\it \_C2}\,{x}^{a}x \left ( -1+x \right ) }{ \left ( -1+x \right ) ^{a}}} \right \} \] Mathematica raw input
DSolve[2*y[x] - a*y'[x] + (1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> ((a^2 + 2*(-1 + x)*x + a*(-1 + 2*x))*(C[1] + ((1 - x)^(1 - a)*x^(1 + a)*C[2])/((-1 + a)*a*(1 + a)*(a^2 + 2*(-1 + x)*x + a*(-1 + 2*x)))))/(4 + 3*a + a^2)}}
Maple raw input
dsolve(x*(1-x)*diff(diff(y(x),x),x)-a*diff(y(x),x)+2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*(a^2+a*(-1+2*x)+2*x^2-2*x)+_C2/((-1+x)^a)*(-1+x)*x^a*x