32. Verify that the function y(t) = 1/5 satisfies the nonhomogeneous linear equation dy (cost)y + }(1 - 1 cost). dt 13

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32 Verify That The Function Y T 1 5 Satisfies The Nonhomogeneous Linear Equation Dy Cost Y 1 1 Cost Dt 13 1 (7.24 KiB) Viewed 55 times

32 Verify That The Function Y T 1 5 Satisfies The Nonhomogeneous Linear Equation Dy Cost Y 1 1 Cost Dt 13 2 (21.23 KiB) Viewed 55 times

32. Verify that the function y(t) = 1/5 satisfies the nonhomogeneous linear equation dy (cost)y + }(1 - 1 cost). dt
13. Consider the nonhomogeneous linear equation dy + 2y = cos 31. dt To find a particular solution, it is pretty clear that our guess must contain a cosine function, but it is not so clear that the guess must also contain a sine function. (a) Guess yp(t) = a cos 3t and substitute this guess into the equation. Is there a value of a such that yp(t) is a solution? (b) Write a brief paragraph explaining why the proper guess for a particular solu- tion is yp(1) = a cos 31 + sin 31.