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
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)
Use the Laplace transform to solve the following initial value
problem,
y′′ − y′ − 30y = δ(t − 7),y(0) = 0, y′(0) = 0.
The solution is of the form ?[g(t)] h(t).
(a) Enter the function g(t) into the answer box below.
(b) Enter the function h(t) into the answer box below.
8)
Use the Laplace transform to solve the given initial-value
problem.
y' − y = 2 cos(4t), y(0) = 0
y(t)=???
9)
Use the Laplace transform to solve the given initial-value
problem.
y'' − 5y' = 8e4t −
4e−t, y(0) = 1, y'(0) = −1
y(t)=?
10)
Use the Laplace transform to solve the given initial-value
problem.
y''' + 2y'' − y' − 2y = sin(4t), y(0) =
0, y'(0) = 0, y''(0) = 1
y(t)=?