Question

Solve the following initial value problem

?′′ + 9? = 10?−?, ?(0) = 0 and ?′(0) = 0

by using the Laplace transform method.

Answer #1

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:
?″−3?′−18?=?(?−9)
?(0)=0, ?′(0)=0
(Notation: write u(t-c) for the
Heaviside step function ??(?)uc(t) with step at ?=?t=c.)

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

Solve the initial value problem using the method of
the laplace transform.
y"+4y'+4y=8t,y(0)=-4,y'(0)=4

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

Solve the initial value problem using
Laplace transform theory.
y”-2y’+10y=24t,
y(0)=0,
y'(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′′−4y′−32y=δ(t−6)y(0)=0,y′(0)=0

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 initial value problem:
y"+4y=4t, y(0)=1, y'(0)=0

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