Question

Problem1-1: Evaluate the time functions of following rational frequency functions. Show all works. F(s)=\frac{s+2}{s^{2}+4 s+3} \rightarrow f(t)=\mathcal{L}^{-1}[F(s)]=? F(s)=\frac{2}{s(s+3)} \rightarrow f(t)=\mathcal{L}^{-1}[F(s)]=? \text { 3) } F(s)=\frac{2^{2}}{s(s+2)^{2}} \rightarrow f(t)=\mathcal{L}^{-1}[F(s)]=\text { ? } \text { 4) } F(s)=\frac{5}{s\left(s^{2}+4 s+5\right)} \rightarrow f(t)=\mathcal{L}^{-1}[F(s)]=? Problem 1. Evaluate y(t) in following Ordinal Differential Equation by utilizing Laplace, inverse-Laplace,Show all works.and Partial-Fraction-Expansion. \text { Given } y^{\prime \prime}(t)-3 y^{\prime}(t)+2 y(t)=4 e^{2 t}, y(t=0)=3, \quad y^{\prime}(t=0)=5 \text {, }

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