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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 A ... Applications, 11th Edition, Single-Term
- 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_forward1. Find the general solution of the equation y" 1 By = 4yarrow_forward
- 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_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_forwardIf 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_forward
- 11.3 11.4: Problem 5 Find the equation of the tangent plane to Z = = e9 + x + x* + 4 at the point (1, 0, 7). = Zarrow_forwardIn 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) = 0arrow_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_forward
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- 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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