1. Use a Laplace transform to solve the initial value problem:
9y" + y = f(t), y(0) = 1, y'(0) = 2
2. Use a Laplace transform to solve the initial value problem:
y" + 4y = sin 4t, y(0) = 1, y'(0) = 2
Take the Laplace transform the following initial value problem
and solve for Y(s)=L{y(t)}
y”-6y’-27y={1, 0<=t<1 ; 0, 1<=t
y(0)=0, y’(0)=0
Y(s)=?
Now find the inverse transform to find y(t)=?
Note:
1/[s(s-9)(s+3)]=(-1/27)/s+(1/36)/(s+3)+(1/108)/(s-9)
Solve for Y(s), the Laplace transform of the solution y(t) to
the initial value problem below. y'''+7y''+4y'-12y= -24, y(0) = 11,
y'(0)= 5, y''(0) = -43