Differential Equations with Boundary-Value Problems (MindTap Course List)
9th Edition
ISBN: 9781305965799
Author: Dennis G. Zill
Publisher: Cengage Learning
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Chapter 9, Problem 2RE
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In Problems 43–46, solve each equation on the interval 0 ≤ θ < 2π43. sin(2θ) + sin (4θ) = 0
44. cos(2θ) + cos(4θ) = 0
45. cos(4θ)) - cos(6θ) = 0
46. sin(4θ) - sin(6θ) = 0
2. Solve for y in terms of x for the following equations:
a) In(1- 2y) = x
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b) In(y - 1) - In 2 = x + In x
c) In(y? - 1) – In(y + 1) = In(sin x)
d) e(In 2)y
1/2
5. Solve the following IVP:
T
cos(t) y/ + sin(t) y = -4 cos (t), y(-)=-
%3D
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Chapter 9 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
Ch. 9.1 - In Problems 110 use the improved Eulers method to...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - Prob. 9ECh. 9.1 - Prob. 10E
Ch. 9.1 - Prob. 11ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Consider the initial-value problem y = 2x 3y + 1,...Ch. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Repeat Problem 19 using the improved Euler’s...Ch. 9.1 - Prob. 21ECh. 9.2 - Use the RK4 method with h = 0.1 to approximate...Ch. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Consider the initial-value problem y′ = 2y, y(0) =...Ch. 9.2 - Prob. 17ECh. 9.2 - Consider the initial-value problem y′ = 2x – 3y +...Ch. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.3 - Prob. 1ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.4 - Use Euler’s method to approximate y(0.2), where...Ch. 9.4 - Prob. 2ECh. 9.4 - Prob. 3ECh. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.5 - Prob. 1ECh. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - Prob. 5ECh. 9.5 - In Problems 1-18 use Definition 7.1.1 to find ℒ{f...Ch. 9.5 - Prob. 7ECh. 9.5 - Prob. 8ECh. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - The electrostatic potential u between two...Ch. 9.5 - Consider the boundary-value problem y″ + xy = 0,...Ch. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - In Problems 1–4 construct a table comparing the...Ch. 9 - In Problems 1–4 construct a table comparing the...Ch. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RE
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- In Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 4. x" + 25x = 90 cos 41; x (0) = 0, x'(0) = 90arrow_forwardIn Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 3. x" + 100x = 225 cos 5t + 300 sin 5t; x(0) = 375, x'(0) = 0arrow_forward2. Graph the functions fi (x)= sin² x, f,(x)=sin² 2xand f(x)= sin² 3x on the interval %3D [0, n]x[-0.5,1.5] with a step size of using Desmos. 4 f should be red. f, should be blue. f. should be green. The Desmos link is www.desmos.com/calculator. Paste your graph in the space below.arrow_forward
- In Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 1. x" + 9x = 10 cos 2t; x(0) = x'(0) = 0arrow_forward(7) Find √ (=//= + 3x + 2) dxarrow_forwardIn Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two oscillations as in Eq. (8). Throughout, primes denote derivatives with respect to time t. In Problems 1–4, graph the solution function x(t) in such a way that you can identify and label (as in Fig. 3.6.2) its pe- riod. 2. x" + 4x = 5 sin 31; x(0) = x'(0) = 0arrow_forward
- In Problems 47–58, use a calculator to solve each equation on the interval 0 … u 6 2p. Round answers to two decimal places. 47. sin θ = 0.4 48. cos θ = 0.6 49. tan θ = 5 50. cot θ = 2 51. cos θ = - 0.9 52. sin θ = - 0.2 53. sec θ = - 4 54. csc θ = - 3 55. 5 tan θ + 9 = 0 56. 4 cot θ = - 5 57. 3 sin θ - 2 = 0 58. 4 cos θ + 3 = 0arrow_forwardIf z = 3x² + y² and (x, y) changes from (1, 3) to (1.05, 3.1), compare the values of Az and dz. (Round your answers to three decimal places.) dz = Az =arrow_forward1. у%3D х3 — 2х2 + 3х — 5 y = 3 – 2x² + 3x – 5 dy - Зx2 — dx 4x + 3arrow_forward
- This question is designed to be answered without a calculator. If f(x) =cos(in x) and f' (x) = g(x) sin(In x), then g(x) = %3D 1 2x 2x Next Mark this and returnarrow_forwardProblem 1. Let X ~ Gamma(a = 2,0 = 2). Compute: (1) VaRo.975(X) (2) ex(9.488) (3) TVAR0.975(X) and TVAR0.95(X)arrow_forward7. Evaluate Soy4 2 - y dy using Gamma/Beta function.arrow_forward
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