Numerical Methods: Euler to Runge–Kutta · Challenge problem

Euler's method with $h = \dfrac{1}{2}$ is applied to $y' = -y$, $y(0) = 1$. The computed values $y_n$ at $t_n = \dfrac{n}{2}$ lie exactly on the solution of a different equation $y' = \mu y$, $y(0) = 1$. Find $\mu$.