Fundamentals of Differential Equations (9th Edition)
9th Edition
ISBN: 9780321977069
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
Publisher: PEARSON
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Suppose solving an equation by Laplace transform results in
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Evaluate y(0).
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1. L( sin(3x) e4*)
d²y
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dx
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Chapter 7 Solutions
Fundamentals of Differential Equations (9th Edition)
Ch. 7.2 - Prob. 1ECh. 7.2 - Prob. 2ECh. 7.2 - Prob. 20ECh. 7.2 - Prob. 28ECh. 7.2 - Prob. 29ECh. 7.4 - In Problems 110, determine the inverse Laplace...Ch. 7.4 - Prob. 3ECh. 7.4 - Prob. 5ECh. 7.4 - Prob. 7ECh. 7.4 - Prob. 9E
Ch. 7.4 - Prob. 11ECh. 7.4 - Prob. 13ECh. 7.4 - In Problems 1120, determine the partial fraction...Ch. 7.4 - Prob. 17ECh. 7.4 - Prob. 19ECh. 7.4 - Prob. 21ECh. 7.4 - Prob. 23ECh. 7.4 - Prob. 25ECh. 7.5 - Prob. 1ECh. 7.5 - Prob. 3ECh. 7.5 - Prob. 5ECh. 7.5 - Prob. 7ECh. 7.5 - Prob. 9ECh. 7.5 - Prob. 11ECh. 7.5 - Prob. 13ECh. 7.5 - Prob. 25ECh. 7.5 - Prob. 27ECh. 7.5 - Prob. 33ECh. 7.5 - Prob. 35ECh. 7.6 - In Problems 14, sketch the graph of the given...Ch. 7.6 - Prob. 3ECh. 7.6 - In Problems 510, express the given function using...Ch. 7.6 - Prob. 7ECh. 7.6 - Prob. 11ECh. 7.6 - Prob. 17ECh. 7.6 - Prob. 19ECh. 7.8 - Prob. 1ECh. 7.8 - Prob. 3ECh. 7.8 - Prob. 5ECh. 7.8 - Prob. 23ECh. 7.10 - In Problems 119, use the method of Laplace...Ch. 7.10 - Prob. 3ECh. 7.10 - Prob. 5ECh. 7.10 - Prob. 7ECh. 7.10 - Prob. 9ECh. 7.10 - Prob. 11ECh. 7.10 - Prob. 13ECh. 7.10 - Prob. 15ECh. 7.10 - Prob. 17ECh. 7.10 - Prob. 19E
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- 4) Find the solution of the initial value problem given below by Laplace transform.arrow_forward9. Use the method of Laplace transform to solve the initial value problem y" + B?y = (a? + B?)eat, y(0) = 1+ a, y/ (0) = a + b8.arrow_forwardExample 5. Solve the initial value problem (IVP) by Laplace transform LUf "(1)) = s'F(s)- sf (0) - y" – y/ – 2y = e", y(0) = 0, 3/ (0) = 1 LIf '(t)] = sF(s)-arrow_forward
- True or False. Two of the methods that can be used to solve the equation below would be the method of undetermined coefficients or Laplace transforms. y" + 2y" – 3y'+ 4y = e- -3t cos 2tarrow_forward6. Solve the initial-value problem Sy" + 2y' + 5y = 3e-2" ly(0) = 1, y'(0) = 1 using the Laplace transform.arrow_forwardSolve the initial value problem below using the method of Laplace transforms. w''-4w'+4w=20t+64, w(-4)= -5, w'(-4)= -4 w(t)= (Answer in terms of e)arrow_forward
- 3. Use a Fourier transform to solve the equation d²y dx2 y= 0 with initial conditions y(0) = yo and y - 0 as x oo,arrow_forward20-33 Use the method of Laplace transforms to solve each IVP. 20. y' +10y=t, y(0)=0 21. y' + 2y = te', y(0) = 2 22. y' 6y=2sin 3t, y(0) = -1arrow_forwardQ-3) Solve the following initial value problem y"+9y = 181 , with y(0)=0 and y'(0)=6 by the method of Laplace Transform.arrow_forward
- 4. a. Prove that 8s +13 L-1 (s² + 4s – 5) } == (7el + 9e-St) by using completing the square method. [8 marks] b. Use Laplace transform to solve the differential equation *(t) – 2kX(t) + k²X(t) = F(t). [12 marks] [Note: Refer to Appendix A: Table of Laplace Transform given on page 4]arrow_forwardfind the Laplace transform Y(s) = ℒ{y} of the solution of the given initial value problem. A method of determining the inverse transform is developed in Section 6.3. You may wish to refer to Problems 16 through 18 in Section 6.1. 17.y′′+4y={1,0≤t<π,0,π≤t<∞;y(0)=1,y′(0)=0arrow_forward8. Use the method of Laplace transform to solve the initial value problem y" - 2ay' + a²y = (a - B)² est, y (0) = 1 + a, y'(0) = aa + B + b. = a = 1, b = 2, a = 10, 3 = 20.arrow_forward
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