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 = 1.04165 (sec), leaf count = 111

$$\left\{\{y(x)\to c_4{e}^{-\frac{\sqrt{3}x}{2}}\sin \left(\frac{x}{2}\right)+c_6{e}^{\frac{\sqrt{3}x}{2}}\sin \left(\frac{x}{2}\right)+c_5\sin (x)+e^{-\frac{\sqrt{3}x}{2}}(c_1{e}^{\sqrt{3}x}+c_3)\cos \left(\frac{x}{2}\right)+(c_2+\frac{1}{4})\cos (x)+\frac{1}{12}x\sin (x)+\frac{1}{126}\cos (2x)\}\right\}$$

✓ Maple : cpu = 0.819 (sec), leaf count = 147

$$\{y\left(x\right)=\frac{1}{504}(504\mathit{\_}\mathit{C}\mathit{3}\cos \left(x/2\right)+504\mathit{\_}\mathit{C}\mathit{4}\sin \left(x/2\right)){\mathrm{e}}^{-\frac{\sqrt{3}x}{2}}+\frac{1}{504}(504\mathit{\_}\mathit{C}\mathit{5}\cos \left(x/2\right)+504\mathit{\_}\mathit{C}\mathit{6}\sin \left(x/2\right)){\mathrm{e}}^{\frac{\sqrt{3}x}{2}}+\frac{{\mathrm{e}}^{-\frac{i}{2}x}}{504}(-21i\sin \left(\frac{x}{2}\right)+33i\sin \left(\frac{3x}{2}\right)+21\cos \left(x/2\right)+9\cos \left(3/2x\right))+\frac{{\mathrm{e}}^{\frac{i}{2}x}}{504}(21i\sin \left(\frac{x}{2}\right)-33i\sin \left(\frac{3x}{2}\right)+21\cos \left(x/2\right)+9\cos \left(3/2x\right))+\frac{\cos \left(2x\right)}{18}+\frac{(504\mathit{\_}\mathit{C}\mathit{1}+21)\cos \left(x\right)}{504}+\frac{(42x+504\mathit{\_}\mathit{C}\mathit{2})\sin \left(x\right)}{504}\}$$