QuestionQuestion

Transcribed TextTranscribed Text

2. Consiler the matrix A - (i )) For and 1, classify equilibiom point the e - 1 - the at. origin for the - Aur. Bonns problem (not gratel): do thesame for all values of c. 3. Consider the equation z' - where A- (a) For c = 1 and c = 1, classify the equilibrium point at the origin. (b) Find a value of c so that the origin is an unstable node. Bonus problem (not graded): classify the critical point for all values of c. 1. Consider the differential equation y" + by + cy - 0 where 0 and c are constants. (a) Turn this equation into a system of first order linear ODEs. (b) Find the characteristic polynomial of the coefficient matrix you found in part (a). llow does this polynomial relate to the original second order equation? a. Consider the system 2((0) - M(t). (a) Tal. 60 be a fixed sulution of this equation. Tf is any sulution LA the inhomogemoos equation, then slow that g(i) - + where is sume solution to the homogemeous system F'(t) - A(t)F(t). (Ilint: consider the difference 5(t) - (b) Conversely, show that it 5(t) is any solution to the bomogeneous equation, then - is a solution to the exquation. (e) Interpret parts (a) and (b) to conclude that the general solution of the inhomogeneous equa- tion ermais the general solution of the homogeneons equitation plus 8 partionlar solution of the equation.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:
    Solution.pdf.

    $35.00
    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Linear Algebra Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats