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 = 200.861 (sec), leaf count = 0 , could not solve

DSolve[Derivative[2][y][x] == -(Csc[x]^2*(-((-1 + a)*a) - (-(1 + a)^2 + a^2*b^2)*Sin[x]^2 - a*(1 + a)*b*Sin[2*x])*y[x]), y[x], x]

✓ Maple : cpu = 1.834 (sec), leaf count = 262

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