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1. Consider the (linear) differential equation = y' + y 2 sin(3t). (a) Use MATLAB to draw a direction field for this equation in the range −1 ≤ t ≤ 5 and −3 ≤ y ≤ 6 (with steps of size 0.2 for both variables). (b) Find the explicit solutions of this differential equation (by hand) satisfying the initial conditions listed below, and use MATLAB to draw their graphs in the same plot as the direction field from (a). You should use a different color for each curve, and these colors should be different than the direction field. i. y(0) = 0 ii. y(0) = 1 iii. y(0) = 2 Comment: You should only submit one plot for this exercise that includes the direction field and the three curves.

1. Consider the (linear) differential equation = y' + y 2 sin(3t). (a) Use MATLAB to draw a direction field for this equation in the range −1 ≤ t ≤ 5 and −3 ≤ y ≤ 6 (with steps of size 0.2 for both variables). (b) Find the explicit solutions of this differential equation (by hand) satisfying the initial conditions listed below, and use MATLAB to draw their graphs in the same plot as the direction field from (a). You should use a different color for each curve, and these colors should be different than the direction field. i. y(0) = 0 ii. y(0) = 1 iii. y(0) = 2 Comment: You should only submit one plot for this exercise that includes the direction field and the three curves.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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please include screenshots of all the MATLAB commands and the outputs

1. Consider the (linear) differential equation = y' + y 2 sin(3t). (a) Use MATLAB to draw a direction field for this equation in the range −1 ≤ t ≤ 5 and −3 ≤ y ≤ 6 (with steps of size 0.2 for both variables). (b) Find the explicit solutions of this differential equation (by hand) satisfying the initial conditions listed below, and use MATLAB to draw their graphs in the same plot as the direction field from (a). You should use a different color for each curve, and these colors should be different than the direction field. i. y(0) = 0 ii. y(0) = 1 iii. y(0) = 2 Comment: You should only submit one plot for this exercise that includes the direction field and the three curves.
Transcribed Image Text:1. Consider the (linear) differential equation = y' + y 2 sin(3t). (a) Use MATLAB to draw a direction field for this equation in the range −1 ≤ t ≤ 5 and −3 ≤ y ≤ 6 (with steps of size 0.2 for both variables). (b) Find the explicit solutions of this differential equation (by hand) satisfying the initial conditions listed below, and use MATLAB to draw their graphs in the same plot as the direction field from (a). You should use a different color for each curve, and these colors should be different than the direction field. i. y(0) = 0 ii. y(0) = 1 iii. y(0) = 2 Comment: You should only submit one plot for this exercise that includes the direction field and the three curves.
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