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
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Chapter 2 Solutions
First Course in Differential Equations (Instructor's)
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