Question

1)using the laplace transform, solve the initial value problem

y1'+y2=0

y1+y2'=2cost

y1(0)=1,y2(0)=0

2)using the convolution, find the inverse transform of (a) F(s)=1/s(s-1) and (b) G(s)=5/(s^2+1)(s^2+25)

Answer #1

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

Find the inverse Laplace transform of the function by using the
convolution theorem.
F(s) =
1
(s + 4)2(s2 + 4)
ℒ−1{F(s)}(t) =
t
0
dτ

9. Determine the solution
to the initial value problem using the Laplace transform and the
convolution integral.
y'’
+ y =
cos(2t); y(0)
= 1, y’(0) = 0.
Evaluate the convolution integral and simplify your solution

Use the Laplace Transform to solve the initial value
problem.
?′′+9?′+18?=3? ,?(0)=2,?′(0)=−1

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 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 convolution theorem to find the inverse Laplace
transform of
H(s) = 1/(s^2+a^2)^2

Solve the initial-value problem. y"-6y'+9y=0; y(0)=2,
y'(0)=3
Given that y1=x2 is a solution to y"+(1/x)
y'-(4/x2) y=0, find a second, linearly independent
solution y2.
Find the Laplace transform. L{t2 *
tet}
Thanks for solving!

find the inverse Laplace transform of the given function.
1. F(s) = (8s2 − 4s + 12)/ s(s2
+ 4)
use the Laplace transform to solve the given initial value
problem.
2. y'' − 2y' + 2y = 0; y(0) = 0, y' (0) = 1

Solve the initial value problem using
Laplace transform theory.
y”-2y’+10y=24t,
y(0)=0,
y'(0)= -1

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 2 minutes ago

asked 9 minutes ago

asked 16 minutes ago

asked 18 minutes ago

asked 29 minutes ago

asked 30 minutes ago

asked 38 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago