Question

laplace transform

y''+y = cos(2t) y(0) =1 y'(0) = -4

Answer #1

y'-2y = 8sin(2t) , y(0) = -4
Use Laplace Transform

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

Use
the Laplace transform to solve:
y’’ + 2y’ + y = e^(2t); y(0) = 0, y’(0) = 0.

Initial Value Problem. Use Laplace transform.
m''(t) - 9*m(t) = cos(2t)
where m(0) = 1 and m'(0) = 3

Find the Laplace Transform of the following functions:
1. e^(-2t+1)
2. cos^2(2t)
3. sin^2(3t)

Solve this Initial Value Problem using the Laplace
transform.
x''(t) - 9 x(t) = cos(2t),
x(0) = 1,
x'(0) = 3

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)=?

Consider the following initial value problem: y′′+49y={2t,0≤t≤7
14, t>7 y(0)=0,y′(0)=0 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)=

Solve the following initial value problem using Laplace
transform
y"+2y'+y=4cos(2t) When y(0)=0 y'(0)=2
Thankyou

Use laplace transform to solve
x'' + 16x = cos(4t)
x(0)= 0
x'(0)= 1

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