(2) Consider the system of linear differential equations: For this system: 2 $2 0 3 x2 (a) Compute the solution explicitly, showing the fundamental matrix of solutions. (b) Draw the phase portrait by solving (c) Calculate the orbits. dx2 3x2 dx1 2x1

Solve the system of linear equations {2x+3y=-15 {4x-3y=10 using the matrix [1/6    1/16]                            [2/9     -1/9]

Solve the first order system of equations in the photograph using the matrix method. The solution must meet the initial conditions.

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Show the complete solution

Find all values of the unknowns which satisfy the matrix equation: [2 + i] [i O 2i 3illz- 11ly| = 2i LO 0

Exercises 1-6 refer to the folkowing systems of equations: (i) dx dt (i) dx 10x (1 – ) – 20xy ху 0.3x = dt 100 dy := 15y (1 -) + 25xy. dt 1. In one of these systems, the prey are very large animals and the predators are very small animals, such as elephants and mosquitoes. Thus it takes many predators to eat one prey, but each prey eaten is a tremendous benefit for the predator population. The other system has very large predators and very small prey. Determine which system is which and provide a justification for your answer

Consider the dynamical system Yk=1 = log (yk) + Yk- Which of the following statements is true about the dynamical system? O The dynamical system has infinite fixed points. The dynamical system has only one fixed points. The dynamical system has.no fixed points.

Solve the system A = 0 using the matrix A

a) Write the above system of linear derivative equations in matrix form. b) Find the general solution of the above system of derivative equations. c) If given the initial requirement f(0) = 3 and g(0) = 0, then get a special solution for the system of the linear publication equation.