Question

The differential equation d2p/dt2=9t has a solution.

(a) 3/(2*t^3)

(b) cannot be determined

(c) no solution

(d) ilaplace(9/s^4)

This question was addressed to me during an interview.

My query is from Laplace Transform topic in section Control System Applications of MATLAB

Answer 1

Correct choice is (b) cannot be determined

Easy explanation: It is not stated whether there are any initial conditions or not for the given differential equation. Hence, it’s not possible to state the solution of the above equation. If the initial conditions are 0, the laplace transform of the given equation yields- s^2p(s)=9/s^2 and a solution is reached by using option ilaplace(9/s^4) in MATLAB and that solution is option 3/(2*t^3). But we cannot talk about a solution until we know about the existence of the initial conditions.