Consider the following Initial Value Problem $($IVP$)$

$y^{\text{'}\text{'}}5y^{\text{'}}4y=0$ with $y(0)=1$ and $y^{\text{'}}(0)=0$

where $y$ is the dependent variable which is a function of the independent variable $t.$

Solve this problem using Laplace Transforms.

Select the equations that are associated with the Laplace transform solution method for this ODE $($there are $3$ correct answers out of $5).$

$y(t)=-\frac{1}{3}(e^{-4}-4e^{-1})$

$Y(s)=\frac{4}{3(s1)}-\frac{1}{3(s4)}$

$Y(s)=\frac{1}{s1}\frac{1}{s4}$

$Y(s)=\frac{s5}{s^{2}5s4}$

$Y(s)=\frac{s1}{s^{2}5s4}$