onsider the initial value problem y" + 16y = 32t, y(0) = 6, y/(0) = 9| 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). s^2Y(s)-6s-9+16Y(s) 32/s^2 help (formulas) b. Solve your equation for Y(s). Y(s) = L {y(t)}=(6s^3+9s^2+32)/(s^2(s^2+16)) c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) = 2t+6cos(7t)+sin(7t)

onsider the initial value problem y" + 16y = 32t, y(0) = 6, y/(0) = 9| 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). s^2Y(s)-6s-9+16Y(s) 32/s^2 help (formulas) b. Solve your equation for Y(s). Y(s) = L {y(t)}=(6s^3+9s^2+32)/(s^2(s^2+16)) c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) = 2t+6cos(7t)+sin(7t)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: y²y" = y³(y')² – yy'

Q: Solve the linear differential equation using Fourier transform.

A: The objective of this question is to solve the given linear differential equation using the Fourier…

Q: Determine the solutions of this differential equation where steps are thorough and explained dy/dx=…

Q: y" - 2y' = -4 y(0) = 0, y'(0) = 4

Q: y' + ) y = xy²

Q: (du/dt)^3 – (du/dt)^2 – 2u = 0

A: Given: (du/dt)^3 – (du/dt)^2 – 2u = 0 Find : solve the differential equation

Q: Transform the differential equation 4y′+2y=t^(5) y(0)=9 into an algebraic equation by taking…

A: The given differential equation .Using the Laplace transformation to find an algebraic equation and…

Q: sin(2t +) dt eu-3 %3D 64

A: Let, I =∫0∞sin2t+π2e2t-3dtApply integration by part ,Ist function = cos(2t) , since sin(π/2+x) =…

Q: y" - y' - 2y = 5 sin x y(0) = 1, y'(0) = −1

Q: Sketch the direction or slope field of the differential equation. Be sure to show any "trends" and…

A: Given,y'=x-2y+1 x y y' 0 0 -2 0 1 -1 2 2 0 2 1 0 3 0 1 4 0 2

Q: • t(dx/dt) = 6te2' + x(2t – 1). %3D |

Q: -16 2/3 = -3 1/2 x -(-4 3/5)

Q: Consider the family of curves y = kx2, where k is a constant. (a) Show that the differential…

A: According to the given information, Consider a family curve:

Q: Transform the differential equation 2y′′−y′+4y=e^(mt) y(0)= 2 y′=5 into an algebraic equation by…

A: (.) Given differential equation is , (.) Some properties of Laplace transform :-

Q: (含) 4 dy The order of the differential equation: d'y +y= 0 is_ dæ3 dx?

A: The Order of a differential equation is the power of the highest derivative. So here the highest…

Q: Draw a direction field and plot (or sketch) several solutions of the differential equation y' = -y(6…

A: Given differential equation is y'=-y(6-ty) Direction field of given equation is

Q: Euler's diFFQ 3. Eqc) ((x) -24(x)=x(y しx1) ucx1-2uしx1 = x 1u(x) )

Q: Determine the differential equation that corresponds to each slope field. No explana- tions…

A: 5. a) The slope field is,dydt=f(y)

Q: 6y"" + 5y"+y' = 0 y (0) = -2, y'(0) = 2, y" (0) = 0

Q: Consider the differential equation: y = 3y - 2x Using a pencil, graph the isoclines. Also, using a…

A: The differential equation isFormulas used,

Q: product rule to 3. Use the substitution uy to solve the differential equation xy' + 5y = 3ay

Q: x+y-8 y' = 3x+3y-4

A: We have the equation y'=x+y-83x+3y-4 or dydx=x+y-83x+3y-4 We need to transform this differential…

Q: 1 - dt -dy=C %3D

Q: (2) Show that Lij = (№²; q) This shows that the derivatives of the normal can be computed knowing…

A: As per the question we have to show the given relation between the derivative of the normal and the…

Q: The slope field for the equation y' = -x -y is shown below On a print out of this slope field,…

A: The slope field for the equation y'=-x-y passes through 1,0

Q: Z = 2xy what will be the partial differential coefficient

Q: dy/dt = y(1-y) y1(0) = 9, y2(0) = -1 What do y1 and y2 mean? The first and second derivatives?

Q: The complementary function(C.F.) of the differential equation(D – 3)°y=sin 3x is O (ci + c2z +…

A: Solution: The objective is to find the complementary solution of the given differential equation

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

100%

At least one of the answers above is NOT correct.
oonsider the initial value problem
y" + 16y = 32t,
y(0) = 6, y (0) = 9.
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).
s^2Y(s)-6s-9+16Y(s)
32/s^2
help (formulas)
b. Solve your equation for Y(s).
Y(s) = L {y(t)}= (6s^3+9s^2+32)(s^2(s^2+16))
c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t).
y(t) = 2t+6cos(7t)+sin(7t)
Note: You can earn partial credit on this problem.

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

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

Similar questions

Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation =k(TA), where T is the temperature of the object after t units of time have passed, A is dT dt the ambient temperature of the object's surroundings, and k is a constant of proportionality. Suppose that a cup of coffee begins at 179 degrees and, after sitting in room temperature of 62 degrees for 14 minutes, the coffee reaches 170 degrees. How long will it take before the coffee reaches 160 degrees? Include at least 2 decimal places in your answer. minutes
stanit 7 Write a differential equation of the form dy = f(x, y) that has y = g(x) as a solution, where the graph of y = g(x) is normal to every curve of the form y = x² + k (k is a constant) where they meet. Write a differential equation that is a mathematical model of the situation described.
One of the following is the slope field for the differential equation Select one alternative: HH tv-51 HII +4) + + H 1 1 11 /3/ 1 / / / / 2/ / / / / / + dy y Which one?
differential equation of this 4 Cx = 2y? + C. family U Pleose create of And make a clossification curve
Solve for Differential Equation using Laplace transform. Give the correct solution and write on a clean paper clearly and readable. Don't forget to box the final answer.
For the differential equation y' = 2y - x, draw line segments representing the slope field at the points (1, 2), (1, 1), (2, 2), and (2, 1).
Consider the differential equation: dy/dx = y(3 - y) 1) Use the slope field plotter to plot different solutions corresponding to A: (0,-2); B: (0,1); C: (0,3); D: (0,4). You can drag each point to the correct place if they're somewhere else on the plane, or click on the point and redefine. Capture a screenshot showing all the solution curves and insert below. f'(x)=y(3-y) Kin/5 -5 Density Length dy de -8 Step size 0.1 Ymas y (3-9) Input. ✔Solution A Solution B Solution C Solution D DCQ= AC: 2) To what value does y(x) approach, as x → ∞, for the solutions corresponding to B,C, and D? To what value does y(x) approach, as x →∞, for the solution corresponding to A? Why is it different from the others? Be specific and answer in terms of what you know about the slope field and its effect on the solution. - 3) Use wolframalpha.com or something similar to find the particular solution corresponding to each of the points A,B,C,D. How is the solution through Point C different from the other…
solve it please before 15 min