Answer:
A solution curve pass through the point (0,4) when [tex]c_{1} = -\frac{4}{3}[/tex].
There is not a solution curve passing through the point(0,1).
Step-by-step explanation:
We have the following solution:
[tex]P(t) = \frac{c_{1}e^{t}}{1 + c_{1}e^{t}}[/tex]
Does any solution curve pass through the point (0, 4)?
We have to see if P = 4 when t = 0.
[tex]P(t) = \frac{c_{1}e^{t}}{1 + c_{1}e^{t}}[/tex]
[tex]4 = \frac{c_{1}}{1 + c_{1}}[/tex]
[tex]4 + 4c_{1} = c_{1}[/tex]
[tex]c_{1} = -\frac{4}{3}[/tex]
A solution curve pass through the point (0,4) when [tex]c_{1} = -\frac{4}{3}[/tex].
Through the point (0, 1)?
Same thing as above
[tex]P(t) = \frac{c_{1}e^{t}}{1 + c_{1}e^{t}}[/tex]
[tex]1 = \frac{c_{1}}{1 + c_{1}}[/tex]
[tex]1 + c_{1} = c_{1}[/tex]
[tex]0c_{1} = 1[/tex]
No solution.
So there is not a solution curve passing through the point(0,1).
