2.1425   ODE No. 1425

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

$$y^{″}(x)=y(x){\csc }^2(x)(-(-a^2{\cos }^2(x)-(3-2a)\cos (x)+3a-3))$$ ✓ Mathematica : cpu = 0.734013 (sec), leaf count = 236

$$\left\{\{y(x)\to \frac{c_2\sqrt{1-\cos (x)}{(-\frac{(2a-1)(\cos (x)+1)}{-2a\cos (x)+\cos (x)+2})}^{a+\frac{1}{2}}(-2a\cos (x)+\cos (x)+2){(1-{\cos }^2(x))}^{-a}{\left(\frac{(2a-1)(\cos (x)-1)}{(2a-1)\cos (x)-2}\right)}^{a-\frac{1}{2}}{F}_1(2a;a-\frac{3}{2},a+\frac{1}{2};2a+1;\frac{3-2a}{-2a\cos (x)+\cos (x)+2},\frac{2a+1}{-2a\cos (x)+\cos (x)+2})\exp (\frac{1}{2}(a-2)\log (1-\cos (x))+\frac{1}{2}a\log (\cos (x)+1))}{2(1-2a{)}^{2}a\sqrt{\cos (x)+1}}+c_1(-2a\cos (x)+\cos (x)+2)\exp (\frac{1}{2}(a-2)\log (1-\cos (x))+\frac{1}{2}a\log (\cos (x)+1))\}\right\}$$

✓ Maple : cpu = 0.441 (sec), leaf count = 101

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}(-2+(2a-1)\cos \left(x\right))\sqrt[4]{2\cos \left(x\right)+2}{(\sin \left(x\right))}^{a-\frac{1}{2}}{(-2\cos \left(x\right)+2)}^{-\frac{3}{4}}+\mathit{\_}\mathit{C}\mathit{2}{}_2\text{F}{}_1(-a-\frac{1}{2},a-\frac{1}{2};-a+\frac{3}{2};\frac{\cos \left(x\right)}{2}+\frac{1}{2}){(\cos \left(x\right)+1)}^{-\frac{1}{4}-\frac{a}{2}}{(2\cos \left(x\right)+2)}^{\frac{3}{4}}{(-\cos \left(x\right)+1)}^{-\frac{1}{4}+\frac{a}{2}}{(-2\cos \left(x\right)+2)}^{-\frac{3}{4}}\}$$