`y=ae^(mx)+be^(-mx)` satisfies which of the following differential equation?

Options

A. `(dy)/(dx)-my=0`
B. `(dy)/(dx)+xy=0`
C. `(d^(2)y)/(dx^(2))+m^(2)y=0`
D. `(d^(2)y)/(dx^(2))-m^(2)y=0`

Answer

D

Explanation

We have, `y=ae^(mx)+be^(-mx)`
`rArr" "(dy)/(dx)=mae^(mx)-mbe^(-mx)`
`rArr" "(d^(2)y)/(dx^(2))=m^(2)(ae^(mx)+be^(-mx))`
`rArr" "(d^(2)y)/(dx^(2))=m^(2)yrArr (d^(2)y)/(dx^(2))-m^(2)y=0`
Hence, option (d) is correct