ODE No. 1580

2.1580 ODE No. 1580

$y^{(6)} (x) + y (x) - \sin (\frac{x}{2}) \sin (\frac{3 x}{2}) = 0$ ✓ Mathematica : cpu = 0.947422 (sec), leaf count = 234

${{y (x) \to c_{4} e^{- \frac{\sqrt{3} x}{2}} \sin (\frac{x}{2}) + c_{6} e^{\frac{\sqrt{3} x}{2}} \sin (\frac{x}{2}) + c_{5} \sin (x) + c_{1} e^{\frac{\sqrt{3} x}{2}} \cos (\frac{x}{2}) + c_{3} e^{- \frac{\sqrt{3} x}{2}} \cos (\frac{x}{2}) + c_{2} \cos (x) + \frac{1}{504} (- 42 \sin^{2} (\frac{x}{2}) - 42 \sin^{2} (x) + 42 x \sin (x) + 42 \sin (\frac{x}{2}) \sin (\frac{3 x}{2}) + 21 \sin (x) \sin (2 x) - 24 \sin (\frac{x}{2}) \sin (\frac{5 x}{2}) - 14 \sin (x) \sin (3 x) - 28 \cos^{4} (x) + 42 \cos^{3} (x) + 63 \cos^{2} (x) + 42 \cos^{2} (\frac{x}{2}) - 7 \cos (3 x) \cos (x) + 42 \cos (\frac{x}{2}) \cos (\frac{3 x}{2}) - 24 \cos (\frac{x}{2}) \cos (\frac{5 x}{2}))}}$

✓ Maple : cpu = 0.709 (sec), leaf count = 164

${y (x) = (\frac{e^{\frac{i}{2} x}}{24} + \frac{e^{- \frac{i}{2} x}}{24}) \cos (\frac{x}{2}) + (\frac{e^{\frac{i}{2} x}}{56} + \frac{e^{- \frac{i}{2} x}}{56}) \cos (\frac{3 x}{2}) + (\frac{i}{24} e^{\frac{i}{2} x} - \frac{i}{24} e^{- \frac{i}{2} x}) \sin (\frac{x}{2}) + (- \frac{11 i}{168} e^{\frac{i}{2} x} + \frac{11 i}{168} e^{- \frac{i}{2} x}) \sin (\frac{3 x}{2}) + \frac{x \sin (x)}{12} + \frac{\cos (x)}{24} + \frac{\cos (2 x)}{18} +_C 1 \cos (x) +_C 2 \sin (x) +_C 3 e^{- \frac{\sqrt{3} x}{2}} \cos (\frac{x}{2}) +_C 4 e^{- \frac{\sqrt{3} x}{2}} \sin (\frac{x}{2}) +_C 5 e^{\frac{\sqrt{3} x}{2}} \cos (\frac{x}{2}) +_C 6 e^{\frac{\sqrt{3} x}{2}} \sin (\frac{x}{2})}$

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