The two functions x(t) and y(t) satisfy the simultaneous equations dx/dt - 2y = -sin(t), dy/dt + 2x = 5cos(t) Find explicit expressions for x(t) and y(t), given that x(0) = 3 and y(0) = 2. Sketch the solution trajectory in the xy-plane for 0 ≤ ? < 2?, showing that the trajectory crosses itself at (0, 1/2) and passes through the points (0, −3) and (0, −1) in the negative x-direction.
The two functions x(t) and y(t) satisfy the simultaneous equations dx/dt - 2y = -sin(t), dy/dt + 2x = 5cos(t) Find explicit expressions for x(t) and y(t), given that x(0) = 3 and y(0) = 2. Sketch the solution trajectory in the xy-plane for 0 ≤ ? < 2?, showing that the trajectory crosses itself at (0, 1/2) and passes through the points (0, −3) and (0, −1) in the negative x-direction.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
The two functions x(t) and y(t) satisfy the simultaneous equations
dx/dt - 2y = -sin(t),
dy/dt + 2x = 5cos(t)
Find explicit expressions for x(t) and y(t), given that x(0) = 3 and y(0) = 2. Sketch the solution
trajectory in the xy-plane for 0 ≤ ? < 2?, showing that the trajectory crosses itself at (0, 1/2) and
passes through the points (0, −3) and (0, −1) in the negative x-direction.
Transcribed Image Text:dx
- 2y = -sin(t),
dt
dy
+ 2x = 5 cos(t).
dt
Expert Solution
Step 1
Given:
dx/dt - 2y = -sin(t),
dy/dt + 2x = 5cos(t)
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