Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below.6, t<1y" - 16y = g(t), y(0) = 5, y'(0) = 5, where g(t) =t, t>1Click here to view the table of Laplace transforms.Click here to view the table of properties of Laplace transforms.Y(s) =O(Type an exact answer in terms of e.)

The initial value problem is y''-16y=g(t) ⋯⋯⋯ (i) y(0)=0, y'(0)=5, where g(t)=6,…

Answered: Solve for Y(s), the Laplace transform…

Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. 6, t<1 y" - 16y = g(t), y(0) = 5, y'(0) = 5, where g(t) = t, t>1

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 77E

See similar textbooks

Related questions

Q: Use the Laplace transform to solve the given differential equation subject to the indicated initial…

Q: 2. Using the Laplace transform, find the solution to the integro-differential equation i(t) – 3r(t)…

Q: (3) Solve the initial value problem using Laplace transform. y + 4y sin 3t, y(0) = 5.

Q: Solution for the initial value problem using laplace transform y' +4y =cos(t); y(0)=0

Q: b) Use the Laplace Transform to solve the following differential equation given the initial…

Q: How do you solve this problem?

Q: Given the differential equation 9e*, y(0) = 0, y'(0) = 5 6t -7t y'' – 9y = - 7e - Apply the Laplace…

A: given data

Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" -…

Q: Solve the differential equation using the Laplace Transform, d'y 104 + 21y = e-l1t, with the initial…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: nd the general solution of differential equation y" - y' olve for the Laplace transform of f(t) =…

A: Given that, y''-y'-6y=0 and f(t)=t5

Q: Q5. Find the Laplace Transform of the functions x(t) and yıt), which satisfy the coupledd first…

Q: y" + 2y' + 5y = e-'sint y(0) = 0, y'(0) = 1 Solve the initial value problem using Laplace transform.

A: Given: Given IVP is y''+2y'+5y=e-tsint,y0=0,y'0=1 we want to solve this IVP by using Laplace…

Q: Find the general solution of differential equation 3y" + 2y' - 8y = 0. Solve for the Laplace…

Q: Q:- solve the differential equation by Laplace transform : y" – 3y' + 2y = e3t %3D Where the initial…

Q: Use Laplace transform to solve the differential equation y"-2y'-3y=0 with the initial conditions…

A: A linear homogeneous ordinary differential equation can be solved using the Laplace transform apart…

Q: Use the Laplace transform to solve the given initial-value problem. y'' − y' = et cos t, y(0) =…

A: Given :y'' − y' = et cos ty(0)=0, y'(0)=0

Q: Knowing that L'{Y (s)} = y(t) , Laplace Transform is applied to a linear differential equation with…

Q: What is the inverse Laplace Transform of a function y(t) if after solving 32-s+3 Differential…

A: Given To determine inverse Laplace transform of a function y(t) Using inverse Laplace transform…

Q: Q3.B. Find a general solution of the following differential equation using Laplace transform. y" -…

Q: Use the Laplace transform to solve the given initial-value problem. y' - y = 2 cos(4t), y(0) = 0…

A: To solve the following problem on lapace transform of differential equations

Q: Given the differential equation and its initial conditions y" + 7y' + 12y = 8 with y(0) = -2 and…

Q: Given the differential equation and its initial conditions y" - 4y' + 5y = 4 e" with y(0) = 2 and…

Q: Find a 4th degree differential equation whose solution y(t) satisfies L{y(t)} = Y (s) = 1/ (s^4 +1)…

A: Formula for Laplace transformations L{0} = 0 L{a·f(t)+b·g(t)} = a·L{f(t)}+b·L{g(t)} here a and b are…

Q: 4) dx Solve the differential equation dt under the initial condition x(0) = M – 2 by Мx — ЗеМt using…

Q: Let Y(s) be the Laplace transform of y(t). Find the equation satisfied by Y(s) when solving the…

A: Introduction: The Laplace transformation is a very important tool in solving an initial value…

Q: 7. When the given differential equation is Solved using Laplace transform Method, the equivalint…

A: Given differential equation isy''+2y'+y=te-tand given conditions are y0=1 and y'0=-2find the…

Q: Solve the initial value problem y" + y'+ 3y = e-3t using the Laplace transform method. Initial…

A: We solve the given initial value problem by using Laplace Transform. We take Laplace Transform both…

Q: Determine the Laplace transform of the differential equation 3y’’’ – y’ = e-3t t5 - 9y’’ + 4y With…

Q: In an integro-differential equation, the unknown dependent variable y appears within an integral,…

A: Given, dydt+4∫0tyt-we-4wdw=3, y0=0 a) Taking Laplace transform of the above equation…

Q: (b) Find x(1) by using Laplace transform and inverse Laplace method of following differential…

Q: Given the differential equation y'' + 5y' – 5y = - 4 sin(4t), y(0) = 2, y'(0) = 0 Apply the Laplace…

Q: Q5) (a) Solve by using Laplace transform the partial differential equation 8², =9. y(0,t)= 0, y(2,t)…

Q: Solve the initial value problem using Laplace Transform Method y'' - 4y = sin 2t ; y(0) = 3,…

A: To solve: The initial value problem using Laplace Transform Method y'' - 4y = sin 2t ; y(0) = 3,…

Q: 8. Use the method of Laplace transform to solve the initial value problem y" – 20y' + a'y = (a –…

Q: y" + 5y' + 4y = 0, y(0) = 1 y'(0) = 0

Q: Use the Laplace transform to solve the given initial-value problem. y' + 3y = e−3t, y(0) = 0

A: NOTE: Refresh your page if you can't see any equations. . take Laplace

Q: Use the Laplace transform to solve the given initial-value problem. y" - y' = e' cos t, y(0) = 0,…

Q: Given the differential equation y'' – 3y' + 3y = 0, y(0) – 1, y'(0) = 1 | Apply the Laplace…

Q: Use the Laplace transform to solve the given initial-value problem. y" - y' = e' cos t, y(0) = 0,…

A: GIVEN: y" - y' = et cost

Q: dy +4 dt -4w y(t - w) e dw = 8, y(0) = 0. a. Use convolution and Laplace transforms to find the…

Q: Given the differential equation y''+2y'+5y=0, y(0)=−2, y'(0)=2 Apply the Laplace Transform and…

A: We have to solve the differential equations by Laplace Transformation.

Q: Use the Laplace transform to solve the given initial-value problem. y''-y'=et cos(t), y(0)=0,…

A: Take Laplace transform on both the sides as follows.

Q: Given the differential equation y"+ 4y' + 2y = - 4 sin(4t), y(0) = - 1, y'(0) = 2 Apply the Laplace…

A: Given - Given the differential equation y'' + 4y' + 2y = -4sin4t, y0 = -1, y'0 = 2 To find - Apply…

Q: What is the initial value problem with the linear ordinary differential equation of the given…

Q: Solve for the solution of the differential equation using Laplace Transform. Find f(1) y" +4y +5y =…

Q: y(T) dr = 4e' cos(2t) COS

A: The solution is given as

Q: Given the differential equation y'' – 4y' + 3y = 0, y(0) = 0, y'(0) - 2 Apply the Laplace Transform…

A: L yn = snY(s) -sn-1y(0) -sn-2y'(0) -...-sy(n-2)(0)-yn-1(0).

Q: Given the differential equation y''+4y'+3y=sin(5t), y(0)=0, y'(0)=1 Apply the Laplace Transform…

Question

Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below.
6, t<1
y" - 16y = g(t), y(0) = 5, y'(0) = 5, where g(t) =
t, t>1
Click here to view the table of Laplace transforms.
Click here to view the table of properties of Laplace transforms.
Y(s) =O
(Type an exact answer in terms of e.)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Laplace Transformation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Solve the initial value problem below using the method of Laplace transforms. w'' - 4w' + 4w=24t+28, w(-2)= -2, w'(-2) = 5 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms.
Apply the translation theorem to find the inverse Laplace transform of the following function. F(s) = %3D 2s - 16 Click the icon to view the table of Laplace transforms. L-^{F(s)} =O (Type an expression using t as the variable.)
Solve the following equations show your solutions. 1. Find the equation of a line perpendicular to y = 1 through A(-1, 1). 2. Find the area of the circle with center at (1, 3) and tangent to the line 5x - 12y - 8 = 0. 3. Determine the Inverse Laplace Transform of F(s) = (s + 2)(e^-s)/(s^2 + 4).
xy3dx+(y+1)e-xdy=0 Laplace transform
Q1) Find Fourier transform for the following functions: a) x(t) = 3+ (sin2wt)²
Q1) Find Fourier transform for the following functions: a) x(t) = 3 + (sin2wt)? b) y(t) = 5. (e-6t). 8(t – 8) + 6u(t + 8) %3D
Find Fourier transform for the following functions:x(t)=3+(sin2wt)2
e^3(t+2)/2. Find laplace transform of the function
Q)find the inverse Laplace transform (3 L-' (P²t1) P-1 (4) L- 2P (P²-1)²
Part II. Find the Inverse Laplace Transform of the following: 8s2-4s+12 1. F(s) s3 +4s
Find the Fourier transform of sinc (2t). (a) 2n A(w/2) 3. (b) п Д(u/4) A(w/8 (d) A(w/16) Moving to the next ouestion.prevents changes to chis anaWer
A) Find and draw the Fourier transform (Choose Two Only): i) f(t) = cosat.cosbt sine ² ( ii) / (t) = sine²