Question
In: Advanced Math
Consider the differential equation y′(t)+9y(t)=−4cos(5t)u(t), with initial condition y(0)=4, A)Find the Laplace transform of the solution...
Consider the differential equation
y′(t)+9y(t)=−4cos(5t)u(t),
with initial condition y(0)=4,
A)Find the Laplace transform of the solution Y(s).Y(s). Write the solution as a single fraction in s.
Y(s)= ______________
B) Find the partial fraction decomposition of Y(s). Enter all factors as first order terms in s, that is, all terms should be of the form (c/(s-p)), where c is a constant and the root p is a constant. Both c and p may be complex.
Y(s)= ____ + ______ +______
C) Find the inverse transform of Y(s). The solution must consist of all real terms.
L−1{Y(s)} = _______________________
Solutions
Colby Messinger answered 2 years agoRelated Solutions
Consider the differential equation y′′(t)+15y′(t)+56y(t)=−210exp(-1t), with initial conditions y(0)=−14, and y′(0)=72. A)Find the Laplace transform of...
Consider the
differential equation
y′′(t)+15y′(t)+56y(t)=−210exp(-1t),
with initial conditions y(0)=−14, and
y′(0)=72.
A)Find the Laplace
transform of the solution Y(s). Write the
solution as a single fraction in s.
Y(s)=
______________
B) Find the partial
fraction decomposition of Y(s). Enter all factors as first order
terms in s, that is, all terms should be of the form
(c/(s-p)), where c is a constant and the root p is a constant. Both
c and p may be complex.
Y(s)= ____ + ______...
Consider the differential equation y′′(t)+15y′(t)+56y(t)=−210exp(-1t), with initial conditions y(0)=−14, and y′(0)=72. A)Find the Laplace transform of...
Consider the differential equation
y′′(t)+15y′(t)+56y(t)=−210exp(-1t),
with initial conditions y(0)=−14, and
y′(0)=72.
A)Find the Laplace
transform of the solution Y(s). Write the
solution as a single fraction in s.
Y(s)=
______________
B) Find the partial
fraction decomposition of Y(s). Enter all factors as first order
terms in s, that is, all terms should be of the form
(c/(s-p)), where c is a constant and the root p is a constant. Both
c and p may be complex.
Y(s)= ____ + ______...
Consider the initial value problem y′′−9y′+20y=0 y(0)=2, y′(0)=4. a. Take the Laplace transform of both sides...
Consider the initial value problem
y′′−9y′+20y=0
y(0)=2, y′(0)=4.
a. 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).
b. Solve your equation for Y(s).
Y(s)=L[y(t)]
c. Take the inverse Laplace transform of both sides of the
previous equation to solve for y(t)....
Solve the laplace transform to solve the initial value problem. y"-6y'+9y=t. Y(0)=0, y'(0)=1
Solve the laplace transform to solve the initial value
problem.
y"-6y'+9y=t. Y(0)=0, y'(0)=1
Solve the differential equation by Laplace transform y^(,,) (t)-2y^' (t)-3y(t)=sint where y^' (0)=0 ,y=(0)=0
Solve the differential equation by Laplace transform
y^(,,) (t)-2y^' (t)-3y(t)=sint where y^' (0)=0
,y=(0)=0
Use the Laplace transform to find the solution y(t) to the IVP y′′+3y′+2y=2e−tt with initial condition...
Use the Laplace transform to find the solution y(t) to the IVP
y′′+3y′+2y=2e−tt with initial condition y(0)=1,y′(0)=2
Use a Laplace Transform technique to find the solution to the differential equation (ie. initial value...
Use a Laplace Transform technique to find the solution to the
differential equation (ie. initial value problem).
y'' + 4y' + 5y = 35e^(-4t)
y(0) = -3
y'(0) = 1
Solve the differential equation using the Laplace transform. y''' + 3y''+2y' = 100e-t , y(0) =...
Solve the differential equation using the Laplace
transform. y''' + 3y''+2y' = 100e-t , y(0) =
0, y'(0) = 0, y''(0) = 0
Consider the system modeled by the differential equation dy/dt - y = t with initial condition y(0) = 1
Consider the system modeled by the differential equation
dy/dt - y = t with initial condition y(0) = 1
the exact solution is given by y(t) = 2et − t − 1
Note, the differential equation dy/dt - y =t can be written as
dy/dt = t + y
using Euler’s approximation of dy/dt = (y(t + Dt) – y(t))/ Dt
(y(t + Dt) – y(t))/ Dt = (t + y)
y(t + Dt) =...
1. Use a Laplace transform to solve the initial value problem: 9y" + y = f(t),...
1. Use a Laplace transform to solve the initial value problem:
9y" + y = f(t), y(0) = 1, y'(0) = 2
2. Use a Laplace transform to solve the initial value problem:
y" + 4y = sin 4t, y(0) = 1, y'(0) = 2
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