Hello, So the question that I was asked to do was :
An aircraft flying under the guidance of a nondirectional beacon (a fixed radio transmitter, abbreviated NDB) moves so that its longitudinal axis always points toward the beacon. A pilot sets out toward an NDB from a point at which the wind is at right angles to the initial direction of the aircraft; the wind maintains this direction. Assume that the wind speed and the speed of the aircraft through the air (its “airspeed”) remain constant. (Keep in mind that the latter is different from the aircraft’s speed with respect to the ground.) Locate the flight in the xy-plane, placing the start of the trip at (2,0) and the destination at (0,0) . Set up the differential equation describing the aircraft’s path over the ground. Hint: dy/dx= dy/dt / dx/dt
and based on this, I derived the equation
But now I have to use any existing software package (MATLAB, Mathematics, WolframAlpha) to solve the D.E. and 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, which I don't know how to do because I've never done it before. So I get that I might have to just type out the differential equation on WolframAlpha, but then how do I find the constant?
An aircraft flying under the guidance of a nondirectional beacon (a fixed radio transmitter, abbreviated NDB) moves so that its longitudinal axis always points toward the beacon. A pilot sets out toward an NDB from a point at which the wind is at right angles to the initial direction of the aircraft; the wind maintains this direction. Assume that the wind speed and the speed of the aircraft through the air (its “airspeed”) remain constant. (Keep in mind that the latter is different from the aircraft’s speed with respect to the ground.) Locate the flight in the xy-plane, placing the start of the trip at (2,0) and the destination at (0,0) . Set up the differential equation describing the aircraft’s path over the ground. Hint: dy/dx= dy/dt / dx/dt
and based on this, I derived the equation
But now I have to use any existing software package (MATLAB, Mathematics, WolframAlpha) to solve the D.E. and 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, which I don't know how to do because I've never done it before. So I get that I might have to just type out the differential equation on WolframAlpha, but then how do I find the constant?