Consider a system of two nonlinear first-order ODEs, where x and y are functions of the independent variable t: 1 1 * = 2 tanh (x) - 2x cos(y) +e+3y-1, y = 3 cosh(x) - 3e²y + 29 y+sin(x). (a) Write down in matrix form of the type X = AX with X = (x, y) the system obtained by linearisation of the above equations around the point x = y = 0. Specify the elements of the matrix A. (b) Find the eigenvalues and eigenvectors of the matrix A obtained in (a). Write down the general solution of the linear system. (c) What type of fixed point is the equilibrium solution x = y = 0? Sketch the phase portrait of the linear system.

Q: Determine if the following statements are true or false. a.) {2} ∈ {1, 2} ________________ b.) {3}…

A: a.) {2} ∈ {1, 2} : FALSE   b.) {3} ∈ {1, {2}, {3}} : TRUE

Q: Prove the following parts of Theorem 2.2.1: For all sets A , B and C A ⊆ B if and only if A ∪ B =…

A:

Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: Question 10: Rewrite the following formal statements in its equivalent informal forms Note: N = set…

A: Square of any negative integer is positive.

Q: Question # 4 Consider a circular table with N > 4 seats. Chris and Sarah are two of N th at ests to…

A: Given a circular table with N seats (N ≥4). Chris and Sarah are two among the N dinner guests,Let us…

Q: Negate the following (in English): a) If it is snowing, then it is cold. b) If x E (0, 1), then x2 <…

A: When we are to negate the statement of the form "If A then B" then the statement should be replaced…

Q: When we are considering n objects taken r at a time, with r . 1, why will the number of combinations…

A: "When we are considering n objects taken r at a time, with r . 1, why will the number of…

Q: [5 -2 31 4 B = 2 -3 2] 1 Q1/ If A = 2 1 Find: -1 Lo] а) 42 b) |A| x B in N

A:

Q: Question 3 [Proof by Contrapositive] Let m,n eZ. Prove that if m +n is odd, then either m or n is…

A:

Q: Prove the following parts of Theorem 2.2.1: For all sets A , B and C A ⊆ A ∪ B

A: Assume xϵA

Q: Exercise 1.2.3. Decide which of the following represent true statements about the nature of sets.…

A:

Q: 5. efine a "condition of special concern." Define two such conditions, and state one possible…

A: Define condition of special concern

Q: A and A' ( its complement) are disjoint a) True b) False

A: Let the universal set be U = {1,2,3,4,5,6} A = {1,2,3}, B={4,5} A' = U - A = {4,5,6}

Q: Given: If A AND B, then C. Given: The if-then statement's reverse isalso correct. If A is True, B is…

A:

Q: 14. A number of grade nine students were surveyed and asked the question "Do you Feel Safe at…

A: Total number of opinions in the survey=6+20+35+29=90 Category Number of opinions corresponding to…

Q: 1. Is the following axiom system consistent/dependent? a. There are six points. b. There are three…

A: Given: The axiom system: (a.) There are six points. (b.) There are three 3-point lines. (c.) There…