2.1088   ODE No. 1088

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

$$4y^{″}(x)+4\tan (x)y^{\prime }(x)+y(x)(-(5{\tan }^2(x)+2))=0$$ ✓ Mathematica : cpu = 0.104075 (sec), leaf count = 180

$$\left\{\{y(x)\to -\frac{(-1{)}^{7/8}{2}^{5/8}{c}_1}{\sqrt[8]{-8{\cos }^2(2x)-16\cos (2x)-8}}+\frac{3(-1{)}^{5/8}{c}_2(4\sqrt[4]{-1}{2}^{3/4}{\sinh }^{-1}\left(\frac{1}{2}\sqrt[4]{-\frac{1}{2}}\sqrt[4]{-8{\cos }^2(2x)-16\cos (2x)-8}\right)-i\sqrt[4]{-8{\cos }^2(2x)-16\cos (2x)-8}\sqrt{8+i\sqrt{2}\sqrt{-8{\cos }^2(2x)-16\cos (2x)-8}})}{8\sqrt[8]{2}\sqrt[8]{-8{\cos }^2(2x)-16\cos (2x)-8}}\}\right\}$$

✓ Maple : cpu = 0.136 (sec), leaf count = 36

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\frac{1}{\sqrt{\cos \left(x\right)}}+\mathit{\_}\mathit{C}\mathit{2}(i\cos \left(x\right)\sin \left(x\right)-\ln (i\cos \left(x\right)+\sin \left(x\right)))\frac{1}{\sqrt{\cos \left(x\right)}}\}$$