Question: Why can't Maple solve this complex-valued differential equation?

I'm attempting to solve the complex-valued differential equation


pde := diff(A(t),t) - I * conjugate(A(t))*A(t)^2 = 0:

However, it seems Maple attempts to solve it using separation of variables and gives

t-Intat(-I/conjugate(_a)/_a^2,_a = A(t))+_C1 = 0

Unless I'm mistaken, a complex integral such as this isn't even defined without a contour.

Working the integral out by hand, I know the solution to be


Is there a trick I'm missing to get Maple to find this solution? Or is this outside the scope of what Maple can handle on it's own?


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