Math 2280 Project 1
Due Wednesday, June 4
Please include all code and graphs necessary to answer each question. The portions
that you are asked to do by hand can be attached seperately. Show all work.
1. Consider the following initial value problem.
dy
dx =4
1 + x2y(0) = 0
a. (By hand) Find the solution yand show that it satisfies y(1) = π.
b. Use Euler’s Method to approximate πwith n= 20 and n= 100 subintervals. Print out the
results for multiples of 0.1.
c. Repeat part b) applying the Improved Euler’s Method.
d. Which method is more efficient? Why?
2. Do #29 in Section 2.4. Do part a) by hand.
3. Do #30 in Section 2.5
4. Do #25 in Section 2.6.
5. Do #5 in Sections 2.4, 2.5, and 2.6. What method would you use to find the exact solution to
the given initial value problem (you do not actually have to work this out)? Why?
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