find the differential equation arising from the relation x=Asin2t+B

Question

this is a math ptoblem from ordinary differential equation.plz tell me the solution of the problem

Answer 1

The given relation, in principle, can be solution to many equations. You have to give certain specification about x(t) and A and B as well. 

If x)t)=Asin2t+B, then

x'=2Acos2t

x''=-4Asin2t=-4(Asin2t+B)-4B=-4x-4B

x''+4x+4B=0

This one of the possible equations. The given relation probably related to mathematical pendulum.