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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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) = 90
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.
3. x" + 100x = 225 cos 5t + 300 sin 5t; x(0) = 375, x'(0) = 0
4. Find a geometric power series for the functions, centered at c = 0 unless a different c is
specified.
a. f(x)=
b. f(x)=· -,c=2
1
2-x
3
2x-1'
f. f(x) =
g. f(x) =
3
2x-1
3x
x²+x-2
Chapter 8 Solutions
Fundamentals of Differential Equations (9th Edition)
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Similar questions
- 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. 2. x" + 4x = 5 sin 31; x(0) = x'(0) = 0arrow_forward1. Given the function f(x) = (=) %3D (a) Find a power-series representation for f(r). n(n +1) (-2)"- (n +2)! (b) Use (a.) to show that f(x) dx = n=1 2.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
- Example 10.4. Find by Taylor's series method, the values of y at x = 0.1 and x = 0.2 to five places of decimals from dyldx = x²y - 1, y(0) = 1.arrow_forward(b) Find the number of terms that are to be retained if an accuracy of 10-10 is required in solving the initial value problem dy = x + y, y (0) =1,xe ]0,1[ dx by Taylors' series.arrow_forward3. Find the Taylor series expansion, up to the seventh (7th) derivative, of the following given functions, at the given centre a: (a) f(x) = -√√x at a = 8; (b) g(x) = cos²x at a = (c) f(x) = 1 (1 + x)³ 3 =; at a = 1;arrow_forward
- Solve the following boundary value problem. Ytt = 49yxx 00; y(0,t) = y(6,t) = 0, y(x,0) = 0, y₁(x,0) = x(6-x) y(x,t) = (Type a series using n as the index variable and 1 as the starting index.)arrow_forward8.5 8.6: Problem 10 Find the first five non-zero terms of power series representation centered at x = O for the function below. 10 f(x) 1 – x3 Answer: f(æ) =O+0+0+D+O- +... What is the interval of convergence? Answer (in interval notation):arrow_forward2. Given that d 1 4- (1 + 3x) = (1 + 3x)² == dx1+3x 3 (1+3x)² g(x) = - term-by-term. find a power series representation for by first representing f(x)= 1 1+3x as a power series, then differentiatingarrow_forward
- 4. Find the first four nonzero terms of the series solution for the following equations. Show the recurrence relation in (a). (a) y" + (x²-1)y' + y = 0 (b) y" + (cos x)y' + (e)y=0arrow_forwardNUMMTD PROBLEM 3: For the function f(x) = 25x3 – 6x² + 7x – 88 , use zero through third-order Taylor Series Expansion to predict f(3) using a base point at x = 1. Compute the true percent relative error for each approximation.arrow_forwardProblem 2: Use the power series representation f (x) = = E-0(-1)"x" = 1 –x + 1 1+x х2 — х3 + for Ixl < 1 to find a power series representation for g(x) = 1 ... on (-1, 1). Determine whether the resulting series converges at the endpoints. (1+x)2arrow_forward
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