4.32.18 $-a{y}^{\prime }(x)+(1-x)x{y}^{″}(x)+2y(x)=0$

ODE
$$-a{y}^{\prime }(x)+(1-x)x{y}^{″}(x)+2y(x)=0$$ ODE Classification

[[_2nd_order, _exact, _linear, _homogeneous]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.190273 (sec), leaf count = 87

$$\left\{\{y(x)\to \frac{(a^2+a(2x-1)+2(x-1)x)(\frac{c_2{x}^{a+1}(1-x{)}^{1-a}}{(a-1)a(a+1)(a^2+a(2x-1)+2(x-1)x)}+c_1)}{a^2+3a+4}\}\right\}$$

Maple ✓
cpu = 0.025 (sec), leaf count = 42

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}(a^2+a(-1+2x)+2x^2-2x)+\frac{\mathit{\_}\mathit{C}\mathit{2}{x}^{a}x(-1+x)}{{(-1+x)}^a}\}$$ 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