How can I get the differential equation from this general solution? I want to find the differential equation which has this general solution: s(t) = a * cos(2t) + bt.

Answer 1

There are an infinite number of solutions because you can differentiate s(t) to obtain s'(t), s''(t), s'''(t) etc and then you could formulate any number of combinations that satisfy the general equation above.

For example, s''(t) + s(t) = -3acos(2t) + bt

or s'(t) = -2asin(2t) + b etc