2. Consider the following ODE: y - 8y' + 16y = 0. (2) [5] (a) Write down and solve the characteristic equation of the ODE.
2. Consider the following ODE: y" - 8y' + 16y = 0. (2) [5] (a) Write down and solve the characteristic equation of the ODE. Then find the gen- eral solution to the ODE. [4] (b) Solve the boundary-value problem with Eq (2) and the boundary condition: y(0) = -3, y (1 ) = e'. [6] (c) Solve the initial-value problem with Eq (2) and the initial condition: y(1) = e', y' (1) = 3ed
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