x1(t) Let x(t) = be a solution to the system of differential equations: x2(t) a(t) x½(t) -23 x1 (t) + 21 x2(t) -28 x1(t) + 26 x2(t) 3 If æ(0) = , find æ(t). 5

Suppose tx1 + 2x2 + sec(t), sin(t)x1+ tx2 – 3. This system of linear differential equations can be put in the form æ' = P(t)æ + g(t). Determine P(t) and g(t). P(t) = g(t) =

Q(1): Find the general solution of y(4) – 5y" + 4y = 10e-3".

Solve 2 []-[² x(t) = y(t) = 2 -5 -4 X x (0) = 8, y(0) = -10

Consider a system of differential equations describing the progress of a disease in a population, given by In our particular case, this is: a) Find the nullclines (simplest form) of this system of differential equations. The x-nullcline is y = x = 3-3xy - 1x y = 3xy - 2y where x (t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of individuals is counted in units of 1,000 individuals. The y-nullclines are y = and x = b) There are two equilibrium points that are biologically meaningful (i.e. whose coordinates are non-negative). They are (x1,9₁) and (x2, y2), where we order them so that x1 < x2. The equilibrium with the smaller x-coordinate is (x₁, y₁) : The equilibrium with the larger x-coordinate is (x2, y₂) = where A = 0 sin (a) c) The linearization of the system of differential equations at the equilibrium (ï1, Y₁) gives a system of the form (+) ¹ (~), f əx ∞ a Ω = A x' G E = F(x, y) for a vector-valued function…