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(Solved): Question 1 (10 points) Let y(t) be a solution of the differential equation y^(')=ry(1-(y)/(K)),r> ...
Question 1 (10 points) Let
y(t)be a solution of the differential equation
y^(')=ry(1-(y)/(K)),r>0,K>0Find the interval
I_(in )where the solution is an increasing function of
t, and the interval
I_(de )where the solution is a decreasing function of
t. Below denotes the empty set.
I_(in )=(-\infty ,0)and
I_(de )=(0,\infty )
I_(in )=(-\infty ,K)and
I_(de )=(K,\infty )
\iota _(in )-(w)and
{(
:+-de-1?,v)\cup (v,?)} None of the options displayed.
I_(in )=(K,\infty )and
I_(de)=(-\infty ,K)
I_(in )=(0,K)and
I_(de)=(-\infty ,0)\cup (K,\infty )and
{(
:_(d)e-1?,v)\cup (v,?)} None of the options displayed.
I_(in )=(K,\infty )and
I_(de)=(-\infty ,K)
I_(in )=(0,K)and
I_(de)=(-\infty ,0)\cup (K,\infty )
I_(in )=(-\infty ,0)\cup (0,\infty )and
I_(in )=(-\infty ,0)\cup (K,\infty )and
I_(de)=(0,K)We need the solution formula to find these intervals. Question 1 (10 points) Let
y(t)be a solution of the differential equation
y^(')=ry(1-(y)/(K)),r>0,K>0Find the interval
I_(in )where the solution is an increasing function of
t, and the interval
I_(de )where the solution is a decreasing function of
t. Below denotes the empty set.
I_(in )=(-\infty ,0)and
I_(de )=(0,\infty )
I_(in )=(-\infty ,K)and
I_(de)=(K,\infty )and
_()de
{(
:-1?,v)\cup (v,?)} None of the options displayed.
I_(in )=(K,\infty )and
I_(de)=(-\infty ,K)
I_(in )=(0,K)and
I_(de)=(-\infty ,0)\cup (K,\infty )