I've been given this questin which is dependant on a previous question that i9 have already completed.
x' = 0.5x(1−(x^2+y^2 )^2)
y' = 0.5y(1−(x^2+y^2 )^2)
Above already given and curves drawn. Now consider the ODE governing evolution of
r(t) = x^2 (t) + y^2 (t). Show that
it then says to ass t'=1 to complete the system when drawing the solution curve and using quiver function.
but i am stuck with what to do, do i use chain rule? and if so how would i apply it, i know i have to use the equations for x' and y' substituted in when i have differentiated r(t) but then i dont know how to use r'=r-r^3.