You must answer questions #1-#4 and either question #5 or question #6. If you answer both question #5 and #6, only the first one will be graded. #1 (a) solve the following initial value problem and give the domain of validity of your solution: dy dx. 1)0( (b) suppose the number of sheep in a field s(t) at time t can be modelled by the equation ds dt. Snks (1) where the constant k > 0 is the growth rate and the constant n > 0 is the field"s carrying capacity. (i) (ii) #2 (a) find a particular solution of the differential equation with b a constant, b x xb x. 2 cos t (b) solve the initial value problem x xb x. #3 (a) find the laplace transform of the function f(t), < t sketched below. (b) for the function f(t) sketched in part (a), solve the following initial value problem: x.
