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Unformatted text preview: ξ = ln x may be of some help. (b) Over what intervals would a solution to the initial value problem exist and be unique? (c) Show that the following initial value problem has no solution y (0) = 1 y ′ (0) = 2 1 (d) Show however that the following problem has a solution but it’s not unique. y (0) bounded Explain these results in the context of the existence and uniqueness theorem. Problem 3 Solve the following system of equations x ′ = 4 2-2-5 3 2-2 4 1 x , x (0) = 3 4 . Problem 4 Using integration find the Laplace transform of (a) cos az , (b) exp( az ) cos bz , (c) z exp( az ) sin bz . Problem 5 Use the method of Laplace transforms to solve the system x ′ = p 4 1-1 2 P x x (0) = x 2...
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- Winter '09
- Boundary value problem, Pierre-Simon Laplace