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Unformatted text preview: Diﬀerential Equations
Homework Assignment 1
Due on Thursday, January 20, at the start of the recitation you are registered in
Your homework should have a cover sheet with the following information: course title,
recitation, last and ﬁrst name (as they appear in the roster), number of homework. If you
use several sheets, please staple them. The problems should be written neatly and in the
order they were assigned.
Problem 1. Draw a direction ﬁeld for the given diﬀerential equation. Based on the direction ﬁeld,
determine the behavior of the solution as t → ∞. Describe how this behavior depends
on the initial value of y at t = 0.
= (y − 1)(y − 3).
Problem 2. Solve the given initial value problem.
y + t3 y y (0) = −2. Problem 3. A 5-gallon bucket is full of pure water. Suppose we begin dumping salt into the bucket
at a rate of 1/4 pounds per minute. Also, we open the spigot so that 1/2 gallons
per minute leaves the bucket, and we add pure water to keep the bucket full. If the
saltwater solution is always well mixed, what is the amount of salt in the bucket after
t minutes? What is the amount of salt in the bucket as t → ∞? ...
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