I am trying to solve a first order differential equation numerically using dsolve. The equation is of the form
dx/dt = k1 x + k2 |x|^2 x
where x(t) is a complex valued function and k1 and k2 are complex constants.
I get the following warning/error from maple10
Warning, abs is not differentiable at non-real arguments
For this equation dsolve only gives me the solution for relatively short times (t ~1 or 2) and I know there is a solution valid at large times >>1.
Obviously I could cast this equation into a system of 2: one for the real part and the other for the imaginary part.
But can I get away with solving just the one equation for x(t)?
If not I would appreciate if someone could explain to me why.