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Unformatted text preview: Homework 7: Diﬀerential Equations
This week, you will submit 2 jpgs and 2 diary ﬁles, one for each problem. Be sure to clean up your diary ﬁle before submitting it. 1. Consider the initial value problem
dy dt = t2 et − 3y with y (0) = 1. • Using dsolve ﬁnd the exact solution to this. • Use myeuler with n = 10 to approximate the solution to approximate the value of y (5) (use the interval [0, 5]). • On the same set of axes, plot the exact solution along with the approximation you found using myeuler. Be sure to use diﬀerent colors and linestyles for each graph. • Determine the error in estimating y (5) using myeuler and put this information on your graph, as was done in the lecture. • Title the graph with your name and “Problem 1” 2. Consider the initial value problem
dy dt = 2t y + et with y (0) = 1. • Attempt to solve this with dsolve. What happens? • Use myeuler with n = 10, n = 20 and n = 50 to approximate the solution on the interval [0, 2]. • Use ode45 to approximate the solution on the interval [0, 2]. • Plot your solution using ode45 along with your 3 solutions using myeuler on the same set of axes. Be sure to use diﬀerent colors and linestyles for each graph. • Title the graph with your name and “Problem 2” ...
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This note was uploaded on 04/19/2011 for the course MATH 21126 taught by Professor Johnson during the Spring '11 term at Carnegie Mellon.
 Spring '11
 Johnson
 Math, matlab, Equations

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