Determine the inverse Laplace Transform of the functionF(s)=−4e−10ss𝐹(𝑠)=−4e−10𝑠𝑠Note: You must use the notation u(t−c)𝑢(𝑡−𝑐) rather than uc(t)𝑢𝑐(𝑡) in order for your answer to be accepted by SOWISO.

Determine the inverse Laplace transform ofG(s)=e−4ss+9𝐺(𝑠)=𝑒−4𝑠𝑠+9Note: You must use the notation u(t−c)𝑢(𝑡−𝑐) rather than uc(t)𝑢𝑐(𝑡) in order for your answer to be accepted by SOWISO.

Determine the inverse Laplace transform ofG(s)=6se−ss2+36𝐺(𝑠)=6𝑠𝑒−𝑠𝑠2+36Note: You must use the notation u(t−c)𝑢(𝑡−𝑐) rather than uc(t)𝑢𝑐(𝑡) in order for your answer to be accepted by SOWISO.

What is the Laplace transform of f(t) = 𝑡2

Determine the Laplace Transform of the functionf(t)=−9δ(t−10)

Determine the Laplace transforms of the initial value problem (IVP)y′′−y′−30y=9u(t−5),y(0)=0,y′(0)=0𝑦″−𝑦′−30𝑦=9𝑢(𝑡−5),𝑦(0)=0,𝑦′(0)=0and obtain an expression for Y(s)=L(y)(t)𝑌(𝑠)=𝐿(𝑦)(𝑡). Do not find the inverse Laplace transform of the resulting equation.