2.1431   ODE No. 1431

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

$$y^{″}(x)=\cot (2x)y^{\prime }(x)-2y(x)$$ ✓ Mathematica : cpu = 0.186659 (sec), leaf count = 80

$$\left\{\{y(x)\to c_1({\cos }^2(x)-\frac{1}{2})-\frac{2}{3}{c}_2{\cos }^{\frac{3}{2}}(x)(2{\cos }^2(x){}_2{F}_1(\frac{1}{4},\frac{3}{4};\frac{7}{4};{\cos }^2(x))-{}_2{F}_1(\frac{1}{4},\frac{3}{4};\frac{7}{4};{\cos }^2(x))+3{(1-{\cos }^2(x))}^{3/4})\}\right\}$$

✓ Maple : cpu = 0.405 (sec), leaf count = 35

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{(\sin \left(2x\right))}^{\frac{3}{4}}\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{P}(\frac{1}{4},\frac{3}{4},\cos \left(2x\right))+\mathit{\_}\mathit{C}\mathit{2}{(\sin \left(2x\right))}^{\frac{3}{4}}\mathit{L}\mathit{e}\mathit{g}\mathit{e}\mathit{n}\mathit{d}\mathit{r}\mathit{e}\mathit{Q}(\frac{1}{4},\frac{3}{4},\cos \left(2x\right))\}$$