Concept explainers
a.
To graph : the solutions that satisfy the initial conditions.
a.
Explanation of Solution
Given information :
the differential equation is
Graph :
From the direction field provided in the question it can be observed that,
The solution of differential equation is
So now for the initial conditions, change the y -intercept of the solution of the differential equation,
Substitute c by
All the solutions are equilibrium solutions, so use plotting approach to make graph,
x | 0 | 0 | 0 | 0 |
y | 0 | 1 | 0.5 | 1.6 |
The graph is obtained as:
Interpretation : from the above graph it can be observed that the graph of all initial conditions are y -intercept change.
b.
To find : the all equilibrium solutions.
b.
Answer to Problem 1E
The solution is
Explanation of Solution
Given information :
the differential equation is
Calculation : from the above part ,
It can be observed that for the given initial conditions the differential equation has equilibrium solutions.
Thus, the solutions is
Chapter 7 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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