2. Consider the homogenous system of differential equations given by: 2 1 x' =(²6_¹¹)* a. Find two solutions to this system. b. Verify that the two solutions you found are fundamental solutions. You must check that the solutions are linearly independent. c. Write the general solution. d. Sketch a phase portrait of the general solution. e. Given the initial condition: x(0) = (2 1)¹ find the coefficients c₁ and c₂. f. Graph out components x₁ (t) and x₂ (t).
2. Consider the homogenous system of differential equations given by: 2 1 x' =(²6_¹¹)* a. Find two solutions to this system. b. Verify that the two solutions you found are fundamental solutions. You must check that the solutions are linearly independent. c. Write the general solution. d. Sketch a phase portrait of the general solution. e. Given the initial condition: x(0) = (2 1)¹ find the coefficients c₁ and c₂. f. Graph out components x₁ (t) and x₂ (t).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Part c,d,e,f please
Transcribed Image Text:2. Consider the homogenous system of differential equations given by:
2 1
x² = (-²6 -¹4) x
a. Find two solutions to this system.
b. Verify that the two solutions you found are fundamental solutions. You must
check that the solutions are linearly independent.
c. Write the general solution.
d.
Sketch a phase portrait of the general solution.
e.
Given the initial condition: x (0) = (2 1)² find the coefficients c₁ and C₂.
f. Graph out components x₁ (t) and x₂ (t).
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