I have an ODE of a complex variable, $$z'(t) = R(t)(c-z(t))$$ where $c$ is a complex constant, $z(0)$ is a complex number and $R(t)$ is an unknown real function with $0<R(t)<\infty$.
Since $R(t)$ is unknown, I do not expect to solve $z(t)$ explicitly. But I think the solution $z(t)$ must lie on the line from $z(0)$ to $c$ as $R(t)>0$, which only controls the speed of $z(t)$ approaching $c$.
To prove the that, I thought about using the mean-value theorem for integral but didn't get fruitful results.
Can anyone please give me a hint?