Find the equation of motion for a fixed particle in a wave

[TheTourist]

A transverse traveling wave is described by

y(x,t)=0.6e^2x-5tcos(5t-2x)​

for x and y measured in cm and t in s
a) Show that y(x,t) satisfies the one-dimensional wave equation, and use this to deduce the wave speed. What is the direction of propagation?
b)USe the work from part (a) to show that the equation of motion for a particle at a fixed x is

a + 10v + 50 y = 0​

Note: a is the second partial derivitive of y w.r.t t, v is the first partial derivitive of y w.r.t. t.

I have done part a) fine but am at a complete loss as to what to do in part b), and it is only worth 2 marks compared to the 8 for part a)

 

[gabbagabbahey]

Basically they just want you to use your expressions for a=\frac{\partial^2 y}{\partial t^2}, and v=\frac{\partial y}{\partial t}...that you calculated in part (a) to show that a+10v+50y=0