I was Unable to find this solution on any other sites. Geogebra has a good graph of the solutions but no way to get to the work. The picture of the textbook and geogebra solution are attached but it would only let me enter a hyperlink. Image 1 is the problem Image 2 is the geogebra solution.This is the problem.
A plane is flying and always pointing towards point (0,0) on an xy plane. Wind is constantly blowing North (positive y direction). The wind speed and speed of the aircraft through the air are constant.
(a) Locate the flight in the xy-plane, placing the start of the trip at (2,0) and the destination at (0,0). Set up a differential equation describing the aircraft's path over the ground.
(b) Make an appropriate substitution and solve this equation.
(c) Use the fact that x = 2 and y = 0 at t = 0 to determine the appropriate value of the arbitrary constant in the solution set.
(d) Solve to get y explicitly in terms of x. Write your solution in terms of a hyperbolic function.
(e) Let gamma be the ratio of windspeed to airspeed. Using a software package, graph solutions for the cases gamma = 0.1, 0.3, 0.5 and 0.7 all on the same set of axes. Interpret these graphs.
(f) Discuss the (terrifying!) cases gamma = 1 and gamma greater then 1.
Physics forum has half answers that do not actually solve the equation. If someone could help work out the first two parts especially that would be much appreciated. Thank you.