Suppose that is a constant (with respect to t) parameter. Consider the ODE: y - 4y...

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Suppose that is a constant (with respect to t) parameter. Consider the ODE: y" - 4y + (4-B)y=0 Classify the values of 3 for which the characteristic equation has: distinct real roots, repeated real roots, and complex roots. (b) Let (t) be the solution of the ODE with initial values (0) = 1, explicit formula for e(t), for every value of 3 (hint: you will need to from the previous part). (c) Let (t) be the solution of the ODE with initial values (0) explicit formula for (t), for every value of 3. - 0, (0) = 0. Find an break it into cases (0) = 1. Find an Suppose that is a constant (with respect to t) parameter. Consider the ODE: y" - 4y + (4-B)y=0 Classify the values of 3 for which the characteristic equation has: distinct real roots, repeated real roots, and complex roots. (b) Let (t) be the solution of the ODE with initial values (0) = 1, explicit formula for e(t), for every value of 3 (hint: you will need to from the previous part). (c) Let (t) be the solution of the ODE with initial values (0) explicit formula for (t), for every value of 3. - 0, (0) = 0. Find an break it into cases (0) = 1. Find an