1.Find the Laplace transformY(s) ={y}

of the solution of the given initial value problem. A method of determining the inverse transform is developed in Section 6.3. You may wish to refer to Problems 21 through 24 in Section 6.1.

y''+4y=t,0t< 1,1,1t<;

y(0) =9,

y'(0) =6

Y(s) =

2.Find the Laplace transformY(s) ={y}

of the solution of the given initial value problem. A method of determining the inverse transform is developed in Section 6.3. You may wish to refer to Problems 21 through 24 in Section 6.1.

y''+9y=1,0t<,0,t<;

y(0) =2,

y'(0) =4

Y(s) =