A wildebeest starts at t = 0 from a point (a, b) in the xy-plane and...

Transcribed Image Text:

A wildebeest starts at t = 0 from a point (a, b) in the xy-plane and moves along the line x = a. A lion, starting from the origin at t = 0 begins the chase, always running in a direction pointing at the wildebeest. The differential equation for the lion's path y(x) is (a x)y" = 1 + y' where is a small parameters (modelling the ratio of the speed of the wildebeest to the speed of the lion). (Note: without loosing generality you may assume that a > 0.) (a) Find the leading order perturbation approximation. Based upon your answer, do you expect the lion to catch the wildebeest? (b) Find the equation for the first correction term in the perturbation approximation, but do not solve. A wildebeest starts at t = 0 from a point (a, b) in the xy-plane and moves along the line x = a. A lion, starting from the origin at t = 0 begins the chase, always running in a direction pointing at the wildebeest. The differential equation for the lion's path y(x) is (a x)y" = 1 + y' where is a small parameters (modelling the ratio of the speed of the wildebeest to the speed of the lion). (Note: without loosing generality you may assume that a > 0.) (a) Find the leading order perturbation approximation. Based upon your answer, do you expect the lion to catch the wildebeest? (b) Find the equation for the first correction term in the perturbation approximation, but do not solve.