Question

If `A` and `B` are arbitrary constants, then find the differential equation corresponding to `y=Acos(x+B)`.

Answer 1

Given equation is
`y=Acos(x+B)`……..`(1)`
`implies (dy)/(dx)=-Asin(x+B)`………..`(2)`
`implies (d^(2)y)/(dx^(2))=-Acos(x+B)`…………`(3)`
The second order derivative is taken because there are two arbitrary constants.
From eqs. `(1)` and `(3)`
`(d^(2)y)/(dx^(2))=-y`.