2.1427   ODE No. 1427

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

$$y^{″}(x)=y(x)(-{\csc }^2(x))(-(a^2{b}^2-(a+1{)}^2){\sin }^2(x)-a(a+1)b\sin (2x)-(a-1)a)$$ ✓ Mathematica : cpu = 0.758874 (sec), leaf count = 129

$$\left\{\{y(x)\to c_2(e^{-abx}{\sin }^{-a-1}(x)+\frac{(2a+1)(-1+e^{2ix})e^{-abx}{\sin }^{a-2(a+1)}(x){}_2{F}_1(1,ia(b+i);iba+a+2;e^{2ix})(b\sin (x)+\cos (x))}{2(a(b-i)-i)})+c_1{e}^{abx}{\sin }^a(x)(b\sin (x)+\cos (x))\}\right\}$$ ✓ Maple : cpu = 1.82 (sec), leaf count = 179

$$\{y\left(x\right)={\mathrm{e}}^{\int \frac{1}{\sin \left(2x\right)(b\sin \left(2x\right)+\cos \left(2x\right)+1)}(2((a+1)\cos \left(2x\right)+a+1/2)b\sin \left(2x\right)-(\cos \left(2x\right)+1)((a{b}^2-a-2)\cos \left(2x\right)-a{b}^2-a+1))\mathrm{d}x}(\int -2{\mathrm{e}}^{-2\int \frac{2((a+1)\cos \left(2x\right)+a+1/2)b\sin \left(2x\right)-(\cos \left(2x\right)+1)((a{b}^2-a-2)\cos \left(2x\right)-a{b}^2-a+1)}{\sin \left(2x\right)(b\sin \left(2x\right)+\cos \left(2x\right)+1)}\mathrm{d}x}\sin \left(2x\right)\mathrm{d}x\mathit{\_}\mathit{C}\mathit{2}+\mathit{\_}\mathit{C}\mathit{1})\frac{1}{\sqrt{\sin \left(2x\right)}}\}$$