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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 )`