Q4RP - 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.

${\mathbf{t}}^{\mathbf{3}}{\left(\frac{{\mathbf{d}}^{\mathbf{3}}\mathbf{x}}{{\mathbf{dt}}^{\mathbf{3}}}\right)}^{\mathbf{2}}\mathbf{+}\mathbf{3}\mathbf{t}\mathbf{-}\mathbf{x}\mathbf{=}\mathbf{0}$

Step-by-Step Solution

Answer

⦁    The Independent variable is t.

⦁    The dependent variable is x.

⦁    The equation is Non-Linear.

Identifying the dependent and independent variables

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

Determining whether the equation is linear or nonlinear

Since the third derivative has power 3, the equation is non-linear.

Hence, the Independent variable is t. The dependent variable is x. The equation is Non-Linear.