2.1428   ODE No. 1428

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

$$y^{″}(x)=y(x)(-{\csc }^2(x))(a{\cos }^2(x)+b{\sin }^2(x)+c)$$ ✓ Mathematica : cpu = 0.389781 (sec), leaf count = 104

$$\left\{\{y(x)\to c_1\sqrt[4]{{\cos }^2(x)-1}{P}_{\frac{1}{2}(2\sqrt{b-a}-1)}^{\frac{1}{2}\sqrt{-4a-4c+1}}(\cos (x))+c_2\sqrt[4]{{\cos }^2(x)-1}{Q}_{\frac{1}{2}(2\sqrt{b-a}-1)}^{\frac{1}{2}\sqrt{-4a-4c+1}}(\cos (x))\}\right\}$$

✓ Maple : cpu = 0.297 (sec), leaf count = 219

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