Q2RP - Fundamentals Of Differential Equations And Boundary Value Problems

Question

In problems 1-6, identify the independent variable, dependent variable, and determine whether the equation is linear or nonlinear.

$\mathbf{3}\mathit{r}\mathbf{-}\mathit{c}\mathit{o}\mathit{s}\mathit{\theta }\frac{\mathbf{d}\mathbf{r}}{\mathbf{d}\mathbf{\theta }}\mathbf{=}\mathit{s}\mathit{i}\mathit{n}\mathit{\theta }$

Step-by-Step Solution

Answer

⦁    The Independent variable is $\theta$ .

⦁    The dependent variable is r.

⦁    The equation is linear.

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  $\mathit{\theta }$.The dependent variable is r. And the equation is linear.