(a)
To find:
(a)
Explanation of Solution
Given information:
The extended logistic differential equation is given as:
with
It is given that
Calculation:
Rewrite the given condition as:
Or
Since
If
Which gives the second term of the differential equation
(b)
To find: If
(b)
Explanation of Solution
Given information:
The extended logistic differential equation is given as:
Calculation:
Substitute the value
Solve the partial fraction
Substitute
Now substitute
Substitute the value of
This is the required result.
(c)
To find: The solution of differential equation in part (b) when
(c)
Answer to Problem 45E
The solution of the differential equation in part ( C) is
Explanation of Solution
Given information:
From part (b) the differential equation is found
Calculation:
In order to solve the differential equation, it can be rewritten as:
Integrate both sides using the formula
Substitute
Substitute the value of
The solution of the differential equation in part (c ) is
(d)
To find: Superimpose of the graph of the solution in part c with
(d)
Answer to Problem 45E
The graph is given.
Explanation of Solution
Given information:
From part (b) the differential equation is found
The solution of this differential equation is
Substitute
The slope field graph is given below:
The graph of the solution
(e)
To find: The general extended equation with restriction
(e)
Answer to Problem 45E
The solution of the differential equation
Explanation of Solution
Given information:
The general differential equation is given as:
This equation can be rewritten as:
Solve the fractional term by partial fraction method.
Substitute
Substitute
Substitute these values in
Now the differential equation can be written as:
Integrate on both sides:
Apply the formula
This is the general solution of the given equation.
Chapter 6 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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