Prove that `y=e^(x)+m` is a solution of the differential equation `(d^(2)y)/(dx^2)-(dy)/(dx)=0`, where `m` is a constant.

Explanation

`y=e^(x)+m`……..`(1)`
Differentiate with respect to `x`
`(dy)/(dx)=e^(x)`……….`(2)`
Again differentiate with respect to `x`
`(d^(2)y)/(dx^(2))=e^(x)`
`implies (d^(2)y)/(dx^(2))=(dy)/(dx)` [From eq. `(2)`]
`implies (d^(2)y)/(dx^(2))-(dy)/(dx)=0`
`:. y=e^(x)+m` is a solution of the given differential equation.