Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
coblem 2. Consider the system of linear differential equations for two real valued functions x(t) and y(t): Sx'(t) = -3x(t) – y(t) ly'(t) = x(t) – y (t) x(t) (a) Write the above system in matrix form X'(t) = AX(t), where X (t) = y(t) (b) Solve your system from part (a) to find two linearly independent vector solutions, 41(t) and 22(t). (c) Directly demonstrate that these two vector solutions e1 (t) and 42(t) are linearly indepen- dent (hint: examine the Wronskian determinant)

coblem 2. Consider the system of linear differential equations for two real valued functions x(t) and y(t): Sx'(t) = -3x(t) – y(t) ly'(t) = x(t) – y (t) x(t) (a) Write the above system in matrix form X'(t) = AX(t), where X (t) = y(t) (b) Solve your system from part (a) to find two linearly independent vector solutions, 41(t) and 22(t). (c) Directly demonstrate that these two vector solutions e1 (t) and 42(t) are linearly indepen- dent (hint: examine the Wronskian determinant)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
See similar textbooks
icon
Related questions
Question
Please solve c,d,e with the answer from a,b that be added in these picture
ols 370a-e2.pdf 2 12 134% Problem 2. Consider the system of linear differential equations for two real valued functions x(t) and y(t): Sx'(t) = -3x(t) – y(t) ly'(t) = x(t) – y(t) (a) Write the above system in matrix form X'(t) = AX(t), where X (t) = (b) Solve your system from part (a) to find two linearly independent vector solutions, P1(t) and e2(t). (c) Directly demonstrate that these two vector solutions 1(t) and 42(t) are linearly indepen- dent (hint: examine the Wronskian determinant). (d) Considering the initial conditions x(0) = 5 and y(0) = 2, find the particular solution to the system of ODES in vector form, and then clearly state the component solutions x(t) and y (t). (e) Plot x(t) and y(t) on the same axis and determine their end behaviors. Problem 3. Consider the second-order linear ODE: x"(t) +64x(t) = 0 where x(0) = ? and x'(0) P Type here to search ASUS ZemBook D F G H. B N M
Transcribed Image Text:ols 370a-e2.pdf 2 12 134% Problem 2. Consider the system of linear differential equations for two real valued functions x(t) and y(t): Sx'(t) = -3x(t) – y(t) ly'(t) = x(t) – y(t) (a) Write the above system in matrix form X'(t) = AX(t), where X (t) = (b) Solve your system from part (a) to find two linearly independent vector solutions, P1(t) and e2(t). (c) Directly demonstrate that these two vector solutions 1(t) and 42(t) are linearly indepen- dent (hint: examine the Wronskian determinant). (d) Considering the initial conditions x(0) = 5 and y(0) = 2, find the particular solution to the system of ODES in vector form, and then clearly state the component solutions x(t) and y (t). (e) Plot x(t) and y(t) on the same axis and determine their end behaviors. Problem 3. Consider the second-order linear ODE: x"(t) +64x(t) = 0 where x(0) = ? and x'(0) P Type here to search ASUS ZemBook D F G H. B N M
eiginvalue: h,= -2, =2 ニ [:] ニ (t)= Azt %3D -2+ ニ General solution: っX() - c, e^* + get*(in, +ve) e; e* ( tv, + vz ) -2t こ
Transcribed Image Text:eiginvalue: h,= -2, =2 ニ [:] ニ (t)= Azt %3D -2+ ニ General solution: っX() - c, e^* + get*(in, +ve) e; e* ( tv, + vz ) -2t こ
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Linear Equations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS