Question

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)=

Answer #1

Consider the following initial value problem:
x′′−3x′−40x=sin(2t),x(0)=4,x′(0)=3
Using X for the Laplace transform of x(t), i.e., X=L{x(t)},,
find the equation you get by taking the Laplace transform of the
differential equation and solve for
X(s)=

Use the Laplace transform to solve the following initial value
problem:
y′′ + 8y ′+ 16y = 0
y(0) = −3 , y′(0) = −3
First, using Y for the Laplace transform of y(t)y, i.e., Y=L{y(t)},
find the equation you get by taking the Laplace transform of the
differential equation
__________________________ = 0
Now solve for Y(s) = ______________________________ and write the
above answer in its partial fraction decomposition, Y(s) = A /
(s+a) + B / ((s+a)^2)
Y(s) =...

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 initial value problem
y′′+4y=16t,y(0)=8,y′(0)=6.y″+4y=16t,y(0)=8,y′(0)=6.
Take the Laplace transform of both sides of the given
differential equation to create the corresponding algebraic
equation. Denote the Laplace transform of y(t) by Y(s). Do not move
any terms from one side of the equation to the other (until you get
to part (b) below).
Solve your equation for Y(s)
Y(s)=L{y(t)}=__________
Take the inverse Laplace transform of both sides of the
previous equation to solve for y(t)y(t).
y(t)=__________

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

Consider the following initial value problem.
y′ + 5y =
{
0
t ≤ 2
10
2 ≤ t < 7
0
7 ≤ t < ∞
y(0) = 5
(a)
Find the Laplace transform of the right hand side of the above
differential equation.
(b)
Let y(t) denote the solution to the above
differential equation, and let Y((s) denote the
Laplace transform of y(t). Find
Y(s).
(c)
By taking the inverse Laplace transform of your answer to (b),
the...

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

Take the Laplace transform of the following initial value
problem and solve for Y(s)=L{y(t)}: y′′−2y′−35y=S(t)y(0)=0,y′(0)=0
where S is a periodic function defined by S(t)={1,0≤t<1 0,
1≤t<2, and S(t+2)=S(t) for all t≥0. Hint: : Use the formula for
the Laplace transform of a periodic function.
Y(s)=

transform the given initial value problem into an algebraic
equation for Y = L{y} in the s-domain. Then find the Laplace
transform of the solution of the initial value problem.
y'' + 4y = 3e^(−2t) * sin 2t,
y(0) = 2, y′(0) = −1

Use the laplace transform to solve for the initial
value problem:
y''+6y'+25y=delta(t-7)
y(0)=0 y'(0)=0

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