Odd constraint problem: Reflected and Transmitted Power of String

1. The problem statement, all variables and given/known data
Given that a string is constrained such that dy/dx = 0 at x = 0 and unconstrained otherwise, what is the reflected and transmitted power?
y is the deflection of the string from the x-axis. y_1 is incident wave, y_r is reflected and y_t is transmitted.

2. Relevant equations

Reflected power, transmitted power have already been derived in terms of impedances.
[tex] Impedance Z = \frac{Driving Force}{string element velocity} [/tex]
Continuity of y and dy/dx.

3. The attempt at a solution
Knowing that y and dy/dx are continuous, I wrote [itex] \frac{\partial y_1}{\partial x} +\frac{\partial y_r}{\partial x} = \frac{\partial y_t}{\partial x} =0 [/itex] at x = 0.

Then I got stuck.

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