Verfify that wave equation `y = e^(2x-5t)` is a soluation to linear equation of the wave (here x & y are in cm & t is in second)

Explanation

`y = e^(2x-5t)`
`(deltay)/(deltat) = - 5e^(2x-5t)`
`rArr (delta^(2)y)/(deltat^(2)) = 25e^(2x-5t) " "…(i)`
Also `(deltay)/(deltax) = 2e^(2x-5t)`
`(delta^(2)y)/(deltax^(2)) = 4e^(2x-5t)" "…(ii)`
`therefore` from (i) and (ii)
`(delta^(2)y)/(deltax^(2)) = (4)/(25) ((delta^(2)y)/(deltat^(2))`
Comparing with lienear wave equation, we can abserve the above function represents a wave travelling with a speed of `(5)/(2)` cm/s.