Question

This is all one question.

3. Suppose Romeo and Juliet's love obeys the following differential equations: :/which has the following eigenvectors: 2 adwth egmao The matrix of this system is with eigenvalue 2, and 1 with eigenvalue-4 We wil use these two eigenvectors to define a new coordinate system, and we will use u and v to represent these coordinates. However, in this problem, we will treat u and v as new variables. Your goal is to rewrite this system of differential equations in terms of these new variables a) Starting with the definition of the coordinates u and v, solve for u and v in terms of R and J to get b) Since R and J are just functions of time, u and v are as well, and taking the derivative of both sides of the two equations above gives R'+J and 'J Substitute the original differential equations into this to get u and v' in terms of R and J 2 c) Now substitute the expressions for R and J (in terms of u and v) from part (a) into your answer from part (b) and simplify. This should give you u and in terms of u and v, d) What is the matrix of the new system of differential equations that you ended up with in part (c)? What do you notice about its form? What do you notice about the specific numbers that appear in it?

Answer 1

可,p3Rーナーーリ -t han 上 W'--. 5.pl.tt7-小(.. R t 3J)-2(3R-J)|ba (au) 2- 2

19アワー41? 0-9