Question

Given the second order initial value problem y′′+y′−6y=5δ(t−2), y(0)=−5, y′(0)=5

Y(s) denote the Laplace transform of y. Then

Y(s)=

Taking the inverse Laplace transform we obtain

y(t)=

y(t)=

Answer #1

Given the second order initial value problem
y′′−3y′=12δ(t−2), y(0)=0, y′(0)=3y″−3y′=12δ(t−2), y(0)=0, y′(0)=3Let
Y(s)Y(s) denote the Laplace transform of yy. Then
Y(s)=Y(s)= .
Taking the inverse Laplace transform we obtain
y(t)=

Given the second order initial value problem
y′′+25y=5δ(t−1), y(0)=2, y′(0)=−10y″+25y=5δ(t−1), y(0)=2, y′(0)=−10Let
Y(s)Y(s) denote the Laplace transform of yy. Then
Y(s)=Y(s)= .
Taking the inverse Laplace transform we obtain y(t)=

Use the Laplace transform to solve the given initial-value
problem.
y'' + 6y' +
34y = δ(t −
π) + δ(t −
7π), y(0) =
1, y'(0) = 0

Use the Laplace Transform to solve the following initial value
problem:
11. y′′ −y′ −6y={0 for0<t<2; e^t for t>2}, y(0)=3,
y′(0)=4

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

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)=__________

Use the Laplace transform to solve the given initial-value
problem. y'' + y = f(t), y(0) = 0, y'(0) = 1, where f(t) = 0, 0 ≤ t
< π 5, π ≤ t < 2π 0, t ≥ 2π

Find the Laplace transform Y(s)=L{y} of the solution of the
given initial value problem.
y′′+9y={t, 0≤t<1 1, 1≤t<∞, y(0)=3, y′(0)=4
Enclose numerators and denominators in parentheses. For example,
(a−b)/(1+n).
Y(s)=

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)=

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