2.1389   ODE No. 1389

1. Problem in Latex
2. Mathematica input
3. Maple input

$$y^{″}(x)=-\frac{y(x)(-4n^{2}x-v(v+1)(x-1{)}^2)}{4(x-1{)}^2{x}^2}-\frac{(3x-1)y^{\prime }(x)}{2(x-1)x}$$ ✓ Mathematica : cpu = 0.379792 (sec), leaf count = 217

$$\left\{\{y(x)\to c_2(-1{)}^{\frac{1}{2}(-2v-3)+1}{x}^{\frac{1}{4}(-2v-3)+1}{e}^{\frac{1}{4}(-2\log (1-x)-\log (x))}(x-1{)}^{\frac{1}{2}(n+\frac{1}{2}(2n+1)+\frac{1}{2}(-2v-3)+v+2)}{}_2{F}_1(\frac{1}{2}(2n+1)+\frac{1}{2}(-2v-3)+1,n+\frac{1}{2}(-2v-3)+v+2;\frac{1}{2}(-2v-3)+2;x)+c_1{x}^{\frac{1}{4}(2v+3)}{e}^{\frac{1}{4}(-2\log (1-x)-\log (x))}(x-1{)}^{\frac{1}{2}(n+\frac{1}{2}(2n+1)+\frac{1}{2}(-2v-3)+v+2)}{}_2{F}_1(\frac{1}{2}(2n+1),n+v+1;\frac{1}{2}(2v+3);x)\}\right\}$$

✓ Maple : cpu = 0.079 (sec), leaf count = 74

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{-\frac{v}{2}}{(x-1)}^{-n}{}_2\text{F}{}_1(-v-n,\frac{1}{2}-n;\frac{1}{2}-v;x)+\mathit{\_}\mathit{C}\mathit{2}{x}^{\frac{1}{2}+\frac{v}{2}}{(x-1)}^{-n}{}_2\text{F}{}_1(\frac{1}{2}-n,v-n+1;\frac{3}{2}+v;x)\}$$