Question: 2. Let A, B. C, D. E E R and A 0. Suppose the Laplace Transform of an ODE is As'Y (s) + Bs(Y(s) +

2. Let A, B. C, D. E E R and A 0. Suppose the Laplace Transform of an ODE is As'Y (s) + Bs(Y(s) + C) + DY (s) + E = kISthe 4s2 + s + 1 (a) Find the initial data for this IVP. (b) Write down the original ODE (untransformed). (c) Is this ODE guaranteed a unique solution? Justify. (d) Suppose A = 1, B = 2, C = -1, D = -2, and E = 5. Finish solving this IVP using Laplace Transforms. (e) Solve this ODE again using one other method. Reconcile your answers. Must both answers be reconcilable? Explain. (f) Prove that there are exactly two linearly independent functions that generate the solution space of this ODE. (g) What sources did you use for this exercise

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