The solution of a differential equation is shown in the figure below. Explain why it can not be the plot of the solution of the following differential equations. You only need to provide one reason (even though there might be several). 4 2 1 2 3 4 5 6 7 8 (a) y' = 1 + y? (b) y = y – 4 (C) y' = (y – 4)(y – 3)(y – 1) (d) zy' = (y – 4)(3 – y)(y – 1)

Answered: The solution of a differential equation is shown in the figure below. Explain why it can not be the plot of the solution of the following differential…

Advanced Engineering Mathematics

10th Edition

ISBN: 9780470458365

Author: Erwin Kreyszig

Publisher: Wiley, John & Sons, Incorporated

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Question

Complete the following question:

The solution of a differential equation is shown in the figure below. Explain why it can not be the
plot of the solution of the following differential equations. You only need to provide one reason
(even though there might be several).
4
2
1
2
3
4
6
7
(a) y' = 1 + y?
(b) y' = y – 4
(c) y' = (y – 4)(y – 3)(y – 1)
(d) z' =
(y – 4)(3 – y)(y – 1)
-

Expert Solution

Step 1

(a)

$y' = 1 + y^{2}$ ( 1 )

In the graph y = 4 is equilibrium point but y = 4 is not an equilibrium point of (1).

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