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Expert-verified Found in: Page 1 ### Fundamentals Of Differential Equations And Boundary Value Problems

Book edition 9th
Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider
Pages 616 pages
ISBN 9780321977069 # In problems 1-6, identify the independent variable, dependent variable, and determine whether the equation is linear or nonlinear.${\mathbf{3}}{\mathbit{r}}{\mathbf{-}}{\mathbit{c}}{\mathbit{o}}{\mathbit{s}}{\mathbit{\theta }}\frac{\mathbf{d}\mathbf{r}}{\mathbf{d}\mathbf{\theta }}{\mathbf{=}}{\mathbit{s}}{\mathbit{i}}{\mathbit{n}}{\mathbit{\theta }}$

⦁ The Independent variable is $\theta$ .

⦁ The dependent variable is r.

⦁ The equation is linear.

See the step by step solution

## Identifying the dependent and independent variables.

Clearly, the independent variable is $\theta$ while the dependent variable is r.

## Determining whether the equation is linear or nonlinear

Since the dependent variable r and its derivatives appear in additive combinations of their first powers, the equation is linear.

Hence, the Independent variable is ${\mathbit{\theta }}$.The dependent variable is r. And the equation is linear. ### Want to see more solutions like these? 