Let

I have shown that the two equations are the real and imaginary parts of a single differential equation for the complex variable

I have evaluated the differential equation for z(t) to get

However, I need to determine the solution to the DE with initial condition I then need to use this to show that the solution of the original equations for x(t) and y(t) with initial conditions

and has both x(t) and y(t) approaching as

Help!