2.1070   ODE No. 1070

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

$$a\tan (x)y^{\prime }(x)+by(x)+y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.352534 (sec), leaf count = 129

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

✓ Maple : cpu = 0.322 (sec), leaf count = 60

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