Lista de Exercícios - Resolução de EDO com Transformada de Laplace - Boyce e DiPrima

Lista 9 Resolução de EDO usando transformada de Laplace extraídos do livro de Boyce e DiPrima In each of Problems 1 through 7 find the inverse Laplace transform of the given function 1 Fs 3 s2 4 2 Fs 4 s 13 3 Fs 2 s2 3s 4 4 Fs 2s 2 s2 2s 5 5 Fs 2s 3 s2 4 6 Fs 8s2 4s 12 ss2 4 7 Fs 1 2s s2 4s 5 In each of Problems 8 through 16 use the Laplace transform to solve the given initial value problem 8 y y 6y 0 y0 1 y0 1 9 y 3y 2y 0 y0 1 y0 0 10 y 2y 2y 0 y0 0 y0 1 11 y 2y 4y 0 y0 2 y0 0 12 y 2y 5y 0 y0 2 y0 1 13 y4 4y 6y 4y y 0 y0 0 y0 1 y0 0 y0 1 14 y4 y 0 y0 1 y0 0 y0 1 y0 0 15 y w2y cos2t w2 4 y0 1 y0 0 16 y 2y 2y et y0 0 y0 1 In each of Problems 17 through 19 find the Laplace transform Ys Ly of the solution of the given initial value problem A method of determining the inverse transform is developed in Section 63 You may wish to refer to Problems 16 through 18 in Section 61 17 y 4y 1 0 t π 0 π t y0 1 y0 0 18 y 4y 1 0 t 1 0 1 t y0 0 y0 0 19 y y 2 t 1 t 2 0 2 t y0 0 y0 0 In each of Problems 1 through 8 a Find the solution of the given initial value problem b Plot a graph of the solution 1 y 2y 2y δt π y0 1 y0 0 2 y 4y δt π δt 2π y0 0 y0 0 3 y 3y 2y δt 5 μt y0 0 y0 12 4 y 2y 3y sin t δt 3π y0 0 y0 0 5 y y δt 2π cos t y0 0 y0 1 6 y 4y 2δt π4 y0 0 y0 0 7 y 2y 2y cos t δt π2 y0 0 y0 0 8 y4 y δt 1 y0 0 y0 0 y0 0 y0 0 edisciplinasuspbr