Form the differential equation of the family of curves `y=Acos2x+Bsin2x ,\ ` where A and B are constants.

Explanation

`y = Acos2x+Bsin2x`

As there are two constants `A` and `B`,
we have to differentiate two times to get the differential equation.

`=>dy/dx = -2Asin2x +2Bcos2x`

`=>(d^2y)/dx^2 = -4Acos2x-4Bcos2x`

`=>(d^2y)/dx^2 = -4(Acos2x+Bcos2x)`

`=>(d^2y)/dx^2 = -4y`

`=>(d^2y)/dx^2 + 4y =0`, which is the required differential equation.