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In Problems 1–10 use the improved Euler’s method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05.
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Chapter 9 Solutions
Bundle: A First Course in Differential Equations with Modeling Applications, Loose-leaf Version, 11th + WebAssign Printed Access Card for Zill's ... Problems, 9th Edition, Single-Term
- Given 3 y' + 2.1 y = 3.4 x 2, y(0) = 4.9, the exact value of y(x = 3.1) most nearly isarrow_forward2. Solve for y in terms of x for the following equations: a) In(1- 2y) = x %3D b) In(y - 1) - In 2 = x + In x c) In(y? - 1) – In(y + 1) = In(sin x) d) e(In 2)y 1/2arrow_forward1. Find the general solution of the equation y" 1 By = 4yarrow_forward
- 2. Suppose P(X|Y) = 1/3 and P(Y) = 1/4. What is P(X NY)?arrow_forwardExample 10.8. Using Euler's method, find an approximate value of y corresponding to x= 1, given that dy/dx = x +y and y= 1 when x = 0.arrow_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. 5. mx" +kx = Fo cos wt with w # wo; x(0) = xo, 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_forwardExample 10.24. If dy = 2ey, y(0) = 2, find y(4) using Adams predictor corrector for- dx mula by calculating y(1), y(2) and y(3) using Euler's modified formula.arrow_forward11.3 11.4: Problem 5 Find the equation of the tangent plane to Z = = e9 + x + x* + 4 at the point (1, 0, 7). = Zarrow_forward
- If the length of a curve from (0,–3) to (3,3) is given by [ V1+(x² – 1)² dx , which of the following could be an equation for this curve? x (A) у%3 3 - 3 (В) у 3D -- 3x – 3 3 (С) у%3D—— х-3 3 (D) y =-+x- 3 3arrow_forwardExample 10.14. Apply Runge's method to find an approximate value of y when x= 0.2, given that dy/dx = x +y and y = 1 when x = 0.arrow_forwardApproximate both solutions of e = 5x to three decimal places (Figure 7). y=e 20- y= 5x 10- FIGURE 7 Graphs of y = e* and y = 5x.arrow_forward
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- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
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