Consider the following initial$-$value problem.

y$+25$y $=$ cos$(5$t$),$ y$(0)=4,$ y$(0)=3$

Take the Laplace transform of the differential equation and solve for

$\{$y$\}.$

$($Write your answer as a function of s$.)$

$\{$y$\}=$

d

Check which variable$($s$)$ should be in your answer.

Use the Laplace transform to solve the given initial$-$value problem. Use the table of Laplace transforms in Appendix C as needed.

y$($t$)=$