Use separation of variables to find product solutions of
The product solutions of the given equation.
Answer to Problem 1RE
When
Explanation of Solution
Given:
The equation is
Calculation:
The given equation is as follows.
Consider the solution of the equation as given below.
Separate the variables of the above equation.
The equation of the variable
The equation of the variable
The solution of the equations can be obtained for various cases considering the value of
When the value of
The general solution of the above equation can be calculated as follows.
Substitute
The general solution of the above equation is as follows.
Substitute the value of
When the value of
The general solution of the equation (3) is as follows.
The general solution of the equation (4) is as follows.
Substitute the value of
Rewrite the term
Thus, when
Want to see more full solutions like this?
Chapter 12 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning