Question

Solve the IVP. Using the Laplace transform.

y'' - (r_{1}+r_{2})y' +
r_{1}r_{2}y = Ae^{at} , y(0)=0, y'(0)=0

Answer #1

Use the Laplace transform to solve the IVP:
y′(t) +y(t) = cos(t),
y(0) = 0.

Use
Laplace transform to solve IVP
2y”+2y’+y=2t , y(0)=1 , y’(0)=-1

Use laplace transform to solve the given IVP
y''-2y'-48y=0
y(0)=13
y'(0)=6

solve the ivp by using the laplace transform
y1' = -y2 , y1 = y2'
y1(0)=1 , y2(0)=-1

Use the definition of the Laplace transform to solve the
IVP:
4y''− 4y' + 5y = δ(t), y(0) = −1, y'(0) = 0.

Given the differential equation
y''−2y'+y=0, y(0)=1, y'(0)=2
Apply the Laplace Transform and solve for Y(s)=L{y}
Y(s) =
Now solve the IVP by using the inverse Laplace Transform
y(t)=L^−1{Y(s)}
y(t) =

Use the Laplace transform to solve the following IVP
y′′ +2y′ +2y=δ(t−5) ,y(0)=1,y′(0)=2,
where δ(t) is the Dirac delta function.

using laplace transform, solve:
y''+4y=8cos2t; y(0)=0, y'(0)=4

Use the Laplace transform to solve the following initial value
problem
y”+4y=cos(8t)
y(0)=0, y’(0)=0
First, use Y for the Laplace transform of 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(t) and its
inverse Laplace transform to find the solution of the IVP:
y(t)=?

solve using the LaPlace transform:
y'' - 6y' - 16y = 8et
y(0) = 2
y'(0) = -1

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