Question

Use the Laplace transform to solve the given equation.

y'' − 8y' + 20y = te^{t}, y(0) =
0, y'(0) = 0

Answer #1

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 given initial value
problem.
y′′−8y′−105y=0; y(0)=8, y′(0)= 76
Enclose arguments of functions in parentheses. For example,
sin(2x).

use the laplace transform to solve initial value
problem
y"+4y'+20y=delta(t-2)
y(0)=0, y'(0)=0
use step t-c for uc(t)

use the Laplace transform to solve the following initial value
problem y”+8y’+25y=&(t-8) y(0)=0 y’(0)=0 use step (t-c) for
uc(t)

Solve the given differential equation by undetermined
coefficients.
y'' − 8y' + 20y = 100x2 − 91xex

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)=?

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

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, given the
initial conditions: y^'' +5y^'+4y = 0 y(0)=1,y^' (0)=0.

use
the laplace transform to solve the following equation
y”-6y’+9y = (t^2)(e^(3t))
y(0)=2
y’(0)=17

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