Mathematics, 30.07.2019 21:30 19wawrzkeek
Consider the differential equation below. (you do not need to solve this differential equation to answer this question.) y' = y^2(y + 4)^3 find the steady states and classify each as stable, semi-stable, or unstable. draw a plot showing some typical solutions. if y(0) = -2 what happens to the solution as time goes to infinity?
Answers: 1
when 
or 
, so we need to check the sign of 
on 3 intervals:
. In particular, let 
. Then 
. Since 
as 
.Suppose 
, say 
. Then 
, so that 
as 
, say 
. Then 
, so that 
as 
-axis indicate the direction of the solution as 
does not converge to the same value from both sides.
, solutions tend toward the line 
solutions diverge to negative infinity.
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Consider the differential equation below. (you do not need to solve this differential equation to an...
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