Science:Math Exam Resources/Courses/MATH215/December 2013/Question 04 (c)/Statement

Let $Y(s)={ℒ}[y]$ be the Laplace transform of the solution $y(t)$ to the following initial value problem:

$\{\begin{array}{l}{y}^{″}-2y^{\prime }+y=g(t),\\ y(0)=0,y^{\prime }(0)=1\end{array}$

where $g(t)$ is the function defined in (a):

$g(t)=\{\begin{array}{l}0,t<1\\ e^{t-1},t\ge 1\end{array}$

(c) Calculate the inverse Laplace transform of Y(s) obtained in (b) to find the solution, y(t), to the IVP in (b).