Question

) Solve the nonhomogeneous system: (t) 5 -2 x(sinh(t) 7.jk(t)-| cosh(t)) 20 An interesting application that leads to a system of differential equations is the study of an arms race. The presentation given here is often called the Richardson model, since it was first proposed by the English metcorologist L.E Richardson. We wish to consider the problem of two countries with expenditures for armaments, x and y, measured in billions of dollars. It is stated that x andy are functions of time, measured in years. Finally, the Richardson model makes the following assumptions 2) The expenditure for armaments by each country will increase at a rate that is proportional to the other country's expenditure. a. b. The expenditure for armaments by each country will decrease at a rate that is proportional to its own expenditure. The rate of change of arms expenditure for a country has a constant component that measures the level of antagonism of that country toward the other c. d. The effects of the three previous assumptions are additive. ах di aypr+r These assumptions lead to the system: The constants a, b, p, and q are dt positive, but the numbers r and s may have any values. Positive values arise if the countries have internal attitudes of distrust for each other, Now, consider the situation: a-6 b-2, p=4, q-3, r-6 апd s=3 with the initial conditions x(o)-0, y(o)-1. i. Write the system to be solved in matrix notation. ii. Write the general solution to this system in matrix form. ii. Impose the initial conditions, and obtain thc solution to the initial value problem iv. Graph the solutions to demonstrate the results of this type of arms race over time. CS Scanned with CamScanner

Please show all work for Number 2. Thank you.

Answer 1

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to-a Shht) C3t?) C142) t 2

& Ct) CIt) Soeval Solul ? s