Concept explainers
To solve:
The initial value problem
To Graph:
The solution of the initial value problem
Solution:
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1) Concept:
The differential equation
Use separation of variables for
Use initial point to get constant of integration.
2) Given:
The initial value problem
3) Calculation:
Can be rewritten as
By the given concept, this is a variables separable differential equation so
Integrating on both sides
Applying initial conditions,
Therefore,
Applying logarithm on both sides
Now to sketch of solution function, first find the domain.
Since logarithmic function is defined for positive values, we get
So the domain is
Conclusion:
The solution of the initial value problem
And sketch of solution function is given below.
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
Calculus (MindTap Course List)
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage