If we have the PDE $ c^2 \frac{{\partial}^2y}{\partial x^2} = \frac{{\partial}^2y}{\partial t^2}$
Make the transformation $ y= z + a(x/L)sin(\omega t) $ to the above PDE to formulate a new PDE.
How would we do this?
So far I have found that $\frac{{\partial}^2y}{\partial x^2} = \frac{{\partial}^2z}{\partial x^2}$.
But I am confused as to how to find $\frac{{\partial}^2z}{\partial t^2}$.