Q5RP - 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.

$\mathbf{6}\mathbf{-}{\mathit{t}}^{\mathbf{3}}\left(\frac{d^{2}v}{d{t}^2}\right)\mathbf{+}\mathbf{3}\mathit{v}\mathbf{-}\mathit{l}\mathit{n}\mathit{t}\mathbf{=}\frac{\mathbf{d}\mathbf{v}}{\mathbf{d}\mathbf{t}}$

Step-by-Step Solution

Answer

⦁    The Independent variable is t.

⦁    The dependent variable is v.

⦁    The equation is Linear.

Identifying the dependent and independent variables

Clearly, the independent variable is t while the dependent variable is v.

Determining whether the equation is linear or nonlinear

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

Hence, the Independent variable is t. The dependent variable is v. The equation is Linear.