Consider the following initial value problemy" +3y' +2y=te²ty(0) = 0y'(0) = -1Denote by Y(s) the Laplace transform of the solution of given initial value problem. What is the correct form of Y(s)?Hint: Take the Laplace transform of both sides of the differential equation in given problem, use the given initial values, and solve the resulting algebraicequation to find Y(s). You can find the table with Laplace transformation formulas in the Resources folder.Your answer:Y(s) =Y(s) =Y(s) =Y(s) =-s²+4s-3(s+1)(s+2)(S-2)²s²-4s+5(s+1)(s+2)(S-2)²-s²+45-5(s+1)(s+2)(S-2)²s²-4s+3(s+1)(s+2)(S-2)²None of the above

Answered: Image /qna-images/answer/96f4023a-c73d-4504-8e60-9b8ada3f8d07.jpg

Answered: Consider the following initial value…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation. (y-x)y=y-x+ 2; y=x+2√x+4 When y=x+2√x+4, y' = Thus, in terms of x, (y-x) = y-x+2= Since the left and right hand sides of the differential equation are equal when x + 2√x+4 is substituted for y. y=x+ 2√x+4 is a solution. Proceed as in Example 6, by considering o simply as a function and give its domain. (Enter your answer using interval notation.) Then by considering as a solution of the differential equation, give at least one interval I of definition, 0 (-8,4) O (-8,-4) 0 (-3,-4) ((-4, 0) 0 (-4,4) Need Help? Wash
5
Consider the initial value problem + 2y = 12t, y(0) = 6. 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). help (formulas) 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). y(t) =
1. Find the general solution of the differential equation y" - y = e²t using (a) a method (without Laplace transform) given in Chapter 3 or 4; (b) the Laplace transform. Hint: In order to use the Laplace transform, you need to use the initial conditions as y(0) = a and y'(0) = b, where a, b are real (arbitrary) constants. 2. Find the solution of the initial value problem y" + 4y = g(t) = { 1° 1 > 16 0. y" + by' + cy= gi(t); y(0) = a, y'(0) = ß on interval 0 to obtain the solution, say, y2(t). (You are able to evaluate y₁ (4) and y(), the initial values at t = 1, since you have obtained y₁ (t) already.) The solution of the original IVP then is y(t) = { vh(t), 0
Consider the following differential equation and initial value. y' = 2x - 3y + 1, y(1) = 6; y(1.2) Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the recursion of (3) in Section 2.6 First, use increment h = 0.1 1.1 Yn + 1 = Yn + hf(xnr Yn) 1.05 1.15 y(1) y(1.2) y(1) y(1.1) 5.99 Then, use increment h = 0.05. (Round your answers to four decimal places.) y(1.2) 5.87 5.9975 5.9425 5.885 6 5.875 (3) 6 X X X X X
What is the resulting differential equation after the initial substitution from the appropriate 2nd order transformation? Do not transpose terms to the other side of the equation. Continue from the solution obtained with the appropriate 2nd order transformation. Assume dy/dx > 0 and x > 0. If x = 1, C1 = 0, and C2 = 0, what is the value of y?
Consider the following differential equation and initial value. y' = 2x - 3y + 1, y(1) = 8; y(1.2) Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the recursion of (3) in Section 2.6 First, use increment h = 0.1 x( Yn + 1 = Yn + hf(xn¹ Yn) 1.1 x( y(1) y(1.2) y(1) Then, use increment h = 0.05. (Round your answers to four decimal places.) y(1.1) 5.9 y(1.2) 4.45 8 8 (3)
The indicated function y₁(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, e-/P(x) dx V₂ = V₁(x) [² Y₂ = y} (x) dx (5) as instructed, to find a second solution y₂(x). (1 - 2x - x²)y" + 2(1+x)y' - 2y = 0; y₁ = x + 1
Consider the following differential equation and initial value. y' = 2x - 3y + 1, y(1) = 4; y(1.2) Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the recursion of (3) in Section 2.6 Yn + 1 = Yn+hf(xn² Yn) (3) First, use increment h = 0.1 x( x y(1) (1 y(1.2) Then, use increment h = 0.05. (Round your answers to four decimal places.) y(1) y(1.1) y(1.2) 4 ]) 4
Problem 3: Use Laplace transform to solve the differential equation: y" + 2y = 8(t-1); y(0) = 0, y'(0) = 1.
Consider the following initial value problem. y" + 10y' + 29y = 8(tn) + 8(t - 7π), y(0) = 1, y'(0) = 0 Find the Laplace transform of the differential equation. (Write your answer as a function of s.) -7μS -TTS e + e + s +1 L{y} (²+10s +29) Use the Laplace transform to solve the given initial-value problem. . Ut- y(t) = 1)+([ ). u(t − n) + ( [
Consider the following initial value problem. у" + 8y' + 25у %3D 6(t — л) + 6(t — 7л), у(0) %3D 1, у'(0) = 0 - Find the Laplace transform of the differential equation. (Write your answer as a function of s.) -TS -7Ts + e + (s + 8) e L{y} (s + 4)² + 32 Use the Laplace transform to solve the given initial-value problem. 4 -4t H )+( že 1,-4(1-1)sin 3(t– n) | × ). a(e - -) + ( e Hcos(3t) × 'e sin( 3t) x -4t. y(t) t - T t - 3

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS