Class Prep for March 30

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Complete all of the non-optional items below, and any of the optional ones you want to complete. Completion of all the non-optional items will earn a Success mark.

Some of these questions have point values; these do not figure into your grade. They are just there to show you which answers are correct and which are not.

Once you submit this form, you should receive a copy of your responses in your GVSU email.

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Your section of MTH 302: *

1 point

03 (2:00-3:50 TR)

04 (4:00-5:50 TR)

(Syllabus/Calendar) Drop-in hours on Tuesdays start at

1 point

11:00am

12:00pm Noon

12:30pm

1:00pm

2:00pm

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(Math review) Consider the system below. Which of the following are straight-line solutions? Select all that apply.

1 point

x(t) = -2, y(t) = 3

x(t) = 1/3 - 2t, y(t) = 3 + 2t

x(t) = -2t + 1/3, y(t) = 3t + 2

x(t) = 1/3 exp(-2t), y = exp(-2t)

x(t) = -2 exp(t/3), y(t) = -2 exp(t)

x(t) = 2 exp(3t), y(t) = exp(3t)

x(t) = 3 exp(2t), y(t) = 3 exp(t)

Videos to watch first: Before proceeding, you will need to watch the three videos below. The total running time is about one hour so you might want to split this up over a 1-3 day period.

Nonhomomgeneous systems part 1: https://gvsu.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=95b57495-47ee-4f55-b6de-afcf01272a5a

Nonhomogeneous systems part 2: https://gvsu.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=79631b83-f9a3-45c8-acbd-afcf01272a4c

Nonhomogeneous systems part 3: https://gvsu.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=7a698ad7-81fa-4b27-9a9e-afcf01272a50

Questions for this lesson

Consider the non-homogeneous system of differential equations below. What exactly makes it non-homogeneous?

1 point

The fact that the y terms are being subtracted on the right

The fact that there are both x and y terms on the right

The fact that it is not just x and y terms on the right but additional numbers added/subtracted

Trick question, this one is actually homogeneous

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Look at the system from the previous question. Which of the following is a particular solution to that system? Select all that apply.

1 point

[5, -10]

[5t, -10t]

[-35/6, -55/6]

[exp(5t), exp(-10t)]

[5 exp(t), -10 exp(t)]

None of these

Suppose you had the general solution to the homogeneous version of the system. How would you find the general solution to the nonhomogeneous system?

Now consider this nonhomogeneous system. Which of the following is the best guess for a particular solution to this system?

1 point

[a,b] where a,b are constants

[At + B, Ct + D] where A,B,C,D are constants

[At^2 + Bt + C, Dt^2 + Et + F] where A, B, C, D, E, F are constants

[A exp(3t) + B, C exp(-t) + D] where A, B, C, D are constants

[A cos(3t) + B, C sin(-t) + D] where A, B, C, D are constants

None of these

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Not actually a question, just a note: Here is a worked-out solution for the previous system: Nonhomogeneous solution.pdf. You'll need to sign into your GV Microsoft account.

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(Optional) What specific math questions do you have over the material in this lesson so far?

1 point

A copy of your responses will be emailed to the address you provided.

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