Question

please anser all and show steps

USANDO TRANSPORMADA DE LAPLACE (7) Resualva la ecuacion diferencial: USANDOTRANFRPMADA DE LAPLACE

Answer 1

y Prime + 6 y prime + 25 y = 1 y(0) = 0, y prime (0) = 0 Apply laplace transform L{y Prime + 6 y prime + 25 y} = L{1} L{y Prime} + 6 L{y prime} + 25 L{y} = L{s} s^2 y(s) - 5y(0) - s prime(0) + 6(sy(s) - y(0)) + 25 y(s) = 1/s s^2 y(s) - s(0) - 0 + 6 (sy(s) - 0) + 25 y(s) = 1/s (s^2 + 6s + 25) y(s) = 1/s y(s) = 1/s(s^2 + 6s + 25) Apply inverse laplace transform L^-1 (y(s)) = L^-1 (1/s(s^2 + 6s + 25)) y(t) = L^-1 (1/25 s - s + 6/2s(s^2 + 6s + 25)) = L^-1 (1/25 s) - L^-1 (s + 6/25(s^2 + 6s + 25)) = 1/25 L^-1 (1/s) - L^-1 (5 + 3 + 3/25 ((s + 3)62 + 4^2)) = 1/25 L^-1 (1/s) - 1/25 L^-1 (s + 3)/(s + 3)^2 + 4^2 + 3/(s + 3)^2 + 4^2)