Concept explainers
Answer Problems 1–12 without referring back to the text. Fill in the blanks or answer true or false.
1. The linear DE, y′ − ky = A, where k and A are constants, is autonomous. The critical point __________ of the equation is a(n) __________ (attractor or repeller) for k > 0 and a(n) __________ (attractor or repeller) for k < 0.
To fill: The blanks with appropriate answer.
Answer to Problem 1RE
The critical point
Explanation of Solution
Given:
The linear differential equation is
Calculation:
The given linear differential equation is,
Simplify the above linear differential equation,
Equate the first derivative to zero to find the critical point.
Thus, the critical point
Want to see more full solutions like this?
Chapter 2 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
- 12 help use variation of parameters to finda general solution to the differntial equation given the function y1 and y2 are linearly independent solutions to the corresponding homogenous equation for t>0arrow_forwardA1 How do I identify the order of differencing (d) for these ARIMA models? Any explanation for how to find d by looking at the equation like in this form would be appreciated. Thanks!arrow_forwardIn this problem, we will use linearization to approximate the solution of et-1 = _t_ +1 which occurs near t=1. 20arrow_forward
- Suppose you ran the regression of the following functional form: yi=b0 +b1xi+ei Where Yi is touchdowns and Xi is rushing yards. Which of the following expressions below tests that “touchdowns and rushing yards are linearly related?” a) a. H0: b1 = 0 H1: b1 ≠ 0 b) b. H0: B0 ≠ 0 H1: B0 = 0 c) c. H0: B1 ≠ 0 H1: B1 = 0 d) d. H0: B1 = 0 H1: B1 ≠ 0arrow_forwardFind the linearization of ƒ(x) = 2/(1 - x) + √(1 + x) - 3.1 at x = 0.arrow_forward2p + q − (α + 1)r = −3p + 3q + 2μr = 8−2p + 4q − (β + 4)r = 11 Find an expression for p in terms of μ using gaussian elimination. Note: α = 0 & β = 6arrow_forward
- Non-Homogenous Linear D.Earrow_forwardChapter 14 Review 53: Find the global extrema of f(x,y) = 2xy−x−y on the domain {y ≤4,y ≥x2}arrow_forwardthe relationship between aphids, A, ( prey) and ladybugs, L, (preditor) can be described as follows: dA/dt=2A=0.01AL dL/dt=-0.5L+0.0001AL a) find the two critical points of the predator-prey equations b) use the chain rule to write dL.dA in terms of L and A c) suppose that at time t=0, there are 1000 aphids and 200 ladybugs, use the Bluffton university slope field generator to graph the slope for the system and the solution curve. let 0 be less than or equal to A who is less than or equal to 15000 and 0 is less than or equal to L which is less than or equal to 400.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage