1) consider the following initial value problem:

y''? 8y'? 9y=sin(6t) y(0)=7,y'(0)=? 4

using y for the laplace transform of y(t), i. e., y=l{y(t)},
find the equation you get by taking the laplace transform of the differential equation and solve for

y(s)=?

2) consider the following initial value problem:

y''? 3y'? 18y=sin(3t) y(0)=7,y'(0)=? 1

using y for the laplace transform of y(t), i. e., y=l{y(t)},
find the equation you get by taking the laplace transform of the differential equation and solve for
y(s)=

3) use the laplace transform to solve the following initial value problem:

y''+4y=cos(8t) y(0)=0,y'(0)=0

first, using y for the laplace transform of y(t), i. e., y=l{y(t)},
find the equation you get by taking the laplace transform of the differential equation and solving for y:

y(s)=

find the partial fraction decomposition of y(s) and its inverse laplace transform to find the solution of the de:

y(t)=