If the roots of the auxiliary equation of a second order linear homogeous ODE are k1 >0 and -k2 < 0, then the solution is x(t) = Ae*it + Be-k2t. For most choice of initial conditions x(0) = x0, i(0) = yo we will have that r(t) → ±0 as t → 0. However, there are some special initial conditions for which x(t) → 0 as t → 0. Find the relationship between ro and yo that ensures this.

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A: A is false  B is false  C is true  D is false  E is false  The detailed solution is as follows…

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A: I have given the answer in the next step. Hope you understand that