Solución
$$\frac{\partial^2 z}{\partial x^2} = -\frac{1}{2}(e^y−e^{−y})senx\\ \frac{\partial^2 z}{\partial y^2} = \frac{1}{2}(e^y−e^{−y})senx\\ \frac{\partial^2 z}{\partial x^2} + \frac{\partial^2 y}{\partial x^2} = 0$$