Question

Consider the differential equation $\frac{dy}{dt} = 12y - 3y^2$. Use a phase-line analysis to find the long-term behavior of $y(t)$ for each of the following given initial conditions. If the answer is infinite, enter oo for $\infty$ or -oo for $-\infty$. If $y(0) = -1$, then as $t$ increases $y(t)$ approaches If $y(0) = 0$, then as $t$ increases $y(t)$ approaches If $y(0) = 2$, then as $t$ increases $y(t)$ approaches If $y(0) = 4$, then as $t$ increases $y(t)$ approaches If $y(0) = 6$, then as $t$ increases $y(t)$ approaches

Name: consider the differential equation fracdydt 12y 3y2 use a phase line analysis to find the long term behavior of yt for each of the following given initial conditions if the answer is infinit 14978
Uploaded: 2023-05-30T16:00:36-08:00
Duration: 4 min 53 s
Channel: Adi S
Description: consider the differential equation fracdydt 12y 3y2 use a phase line analysis to find the long term behavior of yt for each of the following given initial conditions if the answer is infinit 14978

          Consider the differential equation $\frac{dy}{dt} = 12y - 3y^2$.

Use a phase-line analysis to find the long-term behavior of $y(t)$ for each of the following given initial conditions. If the answer is infinite, enter oo for $\infty$ or -oo for $-\infty$.

If $y(0) = -1$, then as $t$ increases $y(t)$ approaches

If $y(0) = 0$, then as $t$ increases $y(t)$ approaches

If $y(0) = 2$, then as $t$ increases $y(t)$ approaches

If $y(0) = 4$, then as $t$ increases $y(t)$ approaches

If $y(0) = 6$, then as $t$ increases $y(t)$ approaches

$consider the differential equation fracdydt 12y 3y2 use a phase line analysis to find the long term behavior of yt for each of the following given initial conditions if the answer is infinit 14978$

Added by Philip C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

05/30/2023

Step 1

$12y - 3y^2 = 0$ $3y(4 - y) = 0$ So, $y = 0$ or $y = 4$. Show more…

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Consider the differential equation $\frac{dy}{dt} = 12y - 3y^2$. Use a phase-line analysis to find the long-term behavior of $y(t)$ for each of the following given initial conditions. If the answer is infinite, enter oo for $\infty$ or -oo for $-\infty$. If $y(0) = -1$, then as $t$ increases $y(t)$ approaches If $y(0) = 0$, then as $t$ increases $y(t)$ approaches If $y(0) = 2$, then as $t$ increases $y(t)$ approaches If $y(0) = 4$, then as $t$ increases $y(t)$ approaches If $y(0) = 6$, then as $t$ increases $y(t)$ approaches