To solve: the given initial value problem by using the separation of variables.
Answer to Problem 7E
The solution is valid for all the real numbers.
Explanation of Solution
Given:
Concept used:
A differential equation of the form
The variables can be separated by writing it in the form
The solution is found by anti differentiating each side with respect to its thusly isolated variable.
Calculation:
Consider the given differential equation,
Now by separating the variables, it follows that
Now by integrating on both sides, it follows that
Put
Therefore, equation (1) becomes
Now by using the given initial conditions, it follows that
Now put
Clearly, the solution is valid for all the real numbers.
Chapter 6 Solutions
CALCULUS-W/XL ACCESS
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning