Consider each of the following problems as illustrations showing that, in a power series solution, we must be cautious about using the general recursion relation between the coefficients for the first few terms of the series.
Solve
If, without thinking carefully, we test the series
Thus we might conclude that the series diverges and that there is no power series solution of this equation. Show why this is wrong, and that the power series solution is
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Mathematical Methods in the Physical Sciences
Additional Math Textbook Solutions
The Heart of Mathematics: An Invitation to Effective Thinking
A Survey of Mathematics with Applications (10th Edition) - Standalone book
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Thinking Mathematically (7th Edition)
Thinking Mathematically (6th Edition)
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning