202_pdfsam_math 54 differential equation solutions odd

202_pdfsam_math 54 differential equation solutions odd -...

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Chapter 4 11. The answer is “no”, because the method of undetermined coefficients cannot be applied to y 0 6 y 0 4 y = 1 t . 13. In the original form, the function sin 2 t does not Ft any of the cases in the method of unde- termined coefficients. But it can be written as sin 2 t =(1 cos 2 t ) / 2, and so 2 t +sin 2 t +3=2 t + 1 cos 2 t 2 +3= ± 2 t + 7 2 ² ± 1 2 cos 2 t ² . Now, the method of undetermined coefficients can be applied to each term in the above di±erence to Fnd a particular solution to the corresponding nonhomogeneous equation, and the di±erence of these particular solutions, by the superposition principle, is a particular solution to the original equation. Thus, the answer is “yes”. 15. “No”, because the given equation is not an equation with constant coefficients. 17. The auxiliary equation in this problem is r 2 1=0w ithroots r = ±
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