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y' = y(4 - y), y(t) = 4/(1+ Ce¬4'), C = 1, 2, . , 5 A general solution may fail to produce all solutions of a differential equation. In Exercise 6, show that y = 0 is a solution of the differential equation, but no value of C in the given general solution will produce this solution.

y' = y(4 - y), y(t) = 4/(1+ Ce¬4'), C = 1, 2, . , 5 A general solution may fail to produce all solutions of a differential equation. In Exercise 6, show that y = 0 is a solution of the differential equation, but no value of C in the given general solution will produce this solution.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer question #7 in the pic attached.

**Instructions for Exercises 3-6** In Exercises 3–6, show that the given solution is a general solution of the differential equation. Use a computer or calculator to sketch the solutions for the given values of the arbitrary constant. Experiment with different intervals for \( t \) until you have a plot that shows what you consider to be the most important behavior of the family. **Exercise 6** 6. \( y' = y(4 - y) \), \( y(t) = \frac{4}{1 + Ce^{-4t}} \), \( C = 1, 2, \ldots, 5 \) **Exercise 7** 7. A general solution may fail to produce all solutions of a differential equation. In Exercise 6, show that \( y = 0 \) is a solution of the differential equation, but no value of \( C \) in the given general solution will produce this solution.
Transcribed Image Text:**Instructions for Exercises 3-6** In Exercises 3–6, show that the given solution is a general solution of the differential equation. Use a computer or calculator to sketch the solutions for the given values of the arbitrary constant. Experiment with different intervals for \( t \) until you have a plot that shows what you consider to be the most important behavior of the family. **Exercise 6** 6. \( y' = y(4 - y) \), \( y(t) = \frac{4}{1 + Ce^{-4t}} \), \( C = 1, 2, \ldots, 5 \) **Exercise 7** 7. A general solution may fail to produce all solutions of a differential equation. In Exercise 6, show that \( y = 0 \) is a solution of the differential equation, but no value of \( C \) in the given general solution will produce this solution.
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