ODE No. 1255

$$a{y}^{\prime }(x)+(x-1)x{y}^{″}(x)-2y(x)=0$$ ✓ Mathematica : cpu = 0.622205 (sec), leaf count = 360

DSolve[-2*y[x] + a*Derivative[1][y][x] + (-1 + x)*x*Derivative[2][y][x] == 0,y[x],x]
 

$$\left\{\{y(x)\to \frac{c_2{x}^a(a^2+2ax-a+2x^2-2x)(1-x{)}^{-a}(-\frac{a{}_2{F}_1(1,-a;1-a;\frac{(-a+\sqrt{1-a^2}+1)(x-1)}{(-a+\sqrt{1-a^2}-1)x})}{{(1-a^2)}^{3/2}}+\frac{a{}_2{F}_1(1,-a;1-a;\frac{(a+\sqrt{1-a^2}-1)(x-1)}{(a+\sqrt{1-a^2}+1)x})}{{(1-a^2)}^{3/2}}+\frac{(x-1)((\sqrt{1-a^2}+1){}_2{F}_1(2,1-a;2-a;\frac{(-a+\sqrt{1-a^2}+1)(x-1)}{(-a+\sqrt{1-a^2}-1)x})-(\sqrt{1-a^2}-1){}_2{F}_1(2,1-a;2-a;\frac{(a+\sqrt{1-a^2}-1)(x-1)}{(a+\sqrt{1-a^2}+1)x}))}{{(a^2-1)}^{2}x})}{2a^2(a^2+3a+4)}+\frac{c_1(a^2+2ax-a+2x^2-2x)}{a^2+3a+4}\}\right\}$$ ✓ Maple : cpu = 0.016 (sec), leaf count = 42

dsolve(x*(x-1)*diff(diff(y(x),x),x)+a*diff(y(x),x)-2*y(x)=0,y(x))
 

$$y\left(x\right)=(a^2+a(2x-1)+2x^2-2x)c_1+c_2{(x-1)}^{-a}(x-1)x^{a}x$$