ASSIGNMENT NUMBER 1, 21.261 Spring 2015
Due Friday, January 23
1. Consider the equation
dy
+ t1/2 y = e2 t
dt
for t > 0. Note that t1/2 is continuous on (0, ), but not on [0, ). Find the
general solution. Determine the behavior of all solutions as t 0+ .

ASSIGNMENT NUMBER 3, 21.261 Spring 2015
Due Friday, February 6
1. Consider the initial value problem
dy
= 2t(y + 1)
dt
y(0) = 1.
First solve this problem. Next compute the Picard iterates for this problem
(dened by
t
2s(yn (s) + 1)ds
yn+1 (t) = 1 +
0
wher

ASSIGNMENT NUMBER 5, 21.261 Spring 2015
Due Friday, February 27
1. Suppose that p(t), q(t), and r(t) are continuous functions and that there
is B > 0 such that |p(t)| B, |q(t)| B, and |r(t)| B for all t. Suppose that
t0 R and
y + p(t)y + q(t)y + r(t)y = 0

ASSIGNMENT NUMBER 2, 21.261 Spring 2015
Due Friday, January 30
1. A population grows according to the logistic law, with a limiting population of 5 108 individuals. When the population is low, it doubles every 40
minutes. What will the population be after

Review Problems, 21.261 Spring 2015
The second test will be in class on Friday, March 27. It will be closed book
and without notes, except for the page on Laplace transforms which has already
been posted on the blackboard site and is included below. These

ASSIGNMENT NUMBER 6, 21.261 Spring 2015
Due Monday, March 16
Note, This assignment would have been due on Friday, March 6 except that
happens to be midsemester break. Hence it will be due on the next class. Assignment 7 will be due on Friday, March 20 as

ASSIGNMENT NUMBER 4, 21.261 Spring 2015
Due Friday, February 20
1. Let Pn denote the amount of money in an account after n months. Assume that P0 = 0 and that the annual interest rate is 10 percent in both parts
below.
A) If monthly deposits of 100 dollar

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