# Science:Math Exam Resources/Courses/MATH152/April 2022/Question B5 (c)/Statement

With the variables ordered , let the matrix of the system of differential equations be . (You don’t need to find .) Consider the following Matlab result:

> [P,D] = eig(A) P = 0.5 - 0.34i 0.5 + 0.34i 0.22 + 0.00i 0.62 + 0.00i 0.62-0.00i 0.85 + 0.00i -0.43 - 0.21i -0.43 + 0.21i 0.47 + 0.00i D = Diagonal Matrix -0.15 + 0.17i 0 0 0 -0.15 - 0.17i 0 0 0 -0.77 + 0.00i

There exist initial conditions that result in a non-oscillating solution (a real solution that does not involve sin and cos). Find one such solution , , that is not oscillating and not zero. Note: you don’t need the results from (a) and (b) to attempt (c).