2.1580   ODE No. 1580

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

$$y^{(6)}(x)+y(x)-\sin \left(\frac{x}{2}\right)\sin \left(\frac{3x}{2}\right)=0$$ ✓ Mathematica : cpu = 2.12085 (sec), leaf count = 234

$$\left\{\{y(x)\to \frac{1}{504}(-42{\sin }^2\left(\frac{x}{2}\right)-42{\sin }^2(x)+42x\sin (x)+42\sin \left(\frac{x}{2}\right)\sin \left(\frac{3x}{2}\right)+21\sin (x)\sin (2x)-24\sin \left(\frac{x}{2}\right)\sin \left(\frac{5x}{2}\right)-14\sin (x)\sin (3x)-28{\cos }^4(x)+42{\cos }^3(x)+63{\cos }^2(x)+42{\cos }^2\left(\frac{x}{2}\right)-7\cos (3x)\cos (x)+42\cos \left(\frac{x}{2}\right)\cos \left(\frac{3x}{2}\right)-24\cos \left(\frac{x}{2}\right)\cos \left(\frac{5x}{2}\right))+c_1{e}^{\frac{\sqrt{3}x}{2}}\cos \left(\frac{x}{2}\right)+c_3{e}^{-\frac{\sqrt{3}x}{2}}\cos \left(\frac{x}{2}\right)+c_2\cos (x)+c_4{e}^{-\frac{\sqrt{3}x}{2}}\sin \left(\frac{x}{2}\right)+c_6{e}^{\frac{\sqrt{3}x}{2}}\sin \left(\frac{x}{2}\right)+c_5\sin (x)\}\right\}$$ ✓ Maple : cpu = 0.612 (sec), leaf count = 154

$$\{y\left(x\right)=\frac{1}{(i\sqrt{3}+3)(i\sqrt{3}-3)(i\sqrt{3}+9)(i\sqrt{3}-9)}((1008\cos \left(x/2\right)\mathit{\_}\mathit{C}\mathit{3}+1008\sin \left(x/2\right)\mathit{\_}\mathit{C}\mathit{4}){\mathrm{e}}^{-\frac{\sqrt{3}x}{2}}+(1008\cos \left(x/2\right)\mathit{\_}\mathit{C}\mathit{5}+1008\sin \left(x/2\right)\mathit{\_}\mathit{C}\mathit{6}){\mathrm{e}}^{\frac{\sqrt{3}x}{2}}+(42\cos \left(x\right)-48)\cos \left(2x\right)-28\cos \left(x\right)\cos \left(3x\right)+42\sin \left(x\right)\sin \left(2x\right)-28\sin \left(3x\right)\sin \left(x\right)+84{(\cos \left(x\right))}^2+(1008\mathit{\_}\mathit{C}\mathit{1}+168)\cos \left(x\right)+84\sin \left(x\right)(x-\sin \left(x\right)+12\mathit{\_}\mathit{C}\mathit{2}))\}$$