Question

(10 points) This problem is related to Problems 8.16-21 in the text. Consider the differential equation y' (t) + 7y(t) = le 4u(t), with initial condition y(0) = 2, Find the Laplace transform of the solution Y(s). Write the solution as a single fraction in s Y(s) = help (formulas) , where cis a Find the partial fraction decomposition of Y(s). Enter all factors as first order terms in s, that is, all terms should be of the form constant and the root p is a constant. Both cand p may be complex. Y(S) = Find the inverse Laplace transform of Y(s). The solution must consist of all real terms. (Remember to use u(t).) y(t) = { } {Y(s)} = help (formulas)

Answer 1

The differential equation is a y'CH + 7y(t) = 16 ut ult) Apply the caplace transform. SY(s) - Y(0) + 748) = 574 Yes (S+ 7) = a + sty as 25+ 9 (5+4) (s+?) Apply the partial fractions: - Y78) = 373 13 + • 13 et st7 sity Apply the inverse Laplace fransform. yen i ett uch & & &t ucts