Question

Consider the initial-value problem $$\frac{dy}{dt} = (3-y)(y+1), \ y(0) = 0.$$ As t→∞ the solution to this initial-value problem approaches 3 from below. Solve, by hand, the initial value problem: $$y(t) = \frac{(3e^{4t}-3)}{(3+e^{4t})}$$ Use Improved Euler's method with n = 8 steps to approximate the solution to the initial-value problem over the time interval 0 ≤ t ≤ 5. You can use this online numerical method widget (opens in new tab). Yo, Y1, Y2,..., Yn = 0, 1.9482, 1.5640, 1.3992, 1.4001, 1.3999, 1.4 (enter as a comma-separated list)

Name: consider the initial value problem fracdydt 3 yy1 y0 0 as t the solution to this initial value problem approaches 3 from below solve by hand the initial value problem yt frac3e4t 33e4t use i 56047
Uploaded: 2022-12-09T17:35:09-08:00
Duration: 2 min 30 s
Channel: Lainey Roebuck
Description: consider the initial value problem fracdydt 3 yy1 y0 0 as t the solution to this initial value problem approaches 3 from below solve by hand the initial value problem yt frac3e4t 33e4t use i 56047

          Consider the initial-value problem
$$\frac{dy}{dt} = (3-y)(y+1), \ y(0) = 0.$$
As t→∞ the solution to this initial-value problem approaches 3 from below.
Solve, by hand, the initial value problem:
$$y(t) = \frac{(3e^{4t}-3)}{(3+e^{4t})}$$
Use Improved Euler's method with n = 8 steps to approximate the solution to the initial-value problem over the time interval 0 ≤ t ≤ 5.
You can use this online numerical method widget (opens in new tab).
Yo, Y1, Y2,..., Yn = 0, 1.9482, 1.5640, 1.3992, 1.4001, 1.3999, 1.4
(enter as a comma-separated list)

$consider the initial value problem fracdydt 3 yy1 y0 0 as t the solution to this initial value problem approaches 3 from below solve by hand the initial value problem yt frac3e4t 33e4t use i 56047$

Added by Tara S.

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