# Consider the following initial value problem. y′ + 5y  = { 0 t  ≤  1 10...

###### Question:

Consider the following initial value problem.

y′ + 5y  =
 { 0 t  ≤  1 10 1  ≤  t  <  6 0 6  ≤  t  <  ∞
y(0)  =  4
 (a) Find the Laplace transform of the right hand side of the above differential equation.
 (b) Let y(t) denote the solution to the above differential equation, and let Y((s) denote the Laplace transform of y(t). Find Y(s).
 (c) By taking the inverse Laplace transform of your answer to (b), the solution y(t) can be written in the form f (t) ?(t − 1) + g (t) ?(t − 6) + h(t). Enter the function f (t) into the answer box below.
 (d) Referring to part (c) above, enter the function g(t) into the answer box below.
 (e) Referring to part (c) above, enter the function h(t) into the answer box below. Consider the following initial value problem. y' + 5y { 0 t = 1 10 1st < 6 0 6 < t < oo y(0) = 4 (a) Find the Laplace transform of the right hand side of the above differential equation. (b) Let y(t) denote the solution to the above differential equation, and let Y((s) denote the Laplace transform of y(t). Find Y(s). (c) By taking the inverse Laplace transform of your answer to (b), the solution y(t) can be written in the form f(t) U(t – 1) + g (t) U(t – 6) + h(t). Enter the function f(t) into the answer box below. (d) Referring to part (c) above, enter the function g(t) into the answer box below. (e) Referring to part (c) above, enter the function h(t) into the answer box below.

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