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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>0

Find 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>0

Find 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 )

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