Q1RP - 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.

$\mathbf{5}\frac{\mathbf{dx}}{\mathbf{dt}}\mathbf{+}\mathbf{5}{\mathbf{x}}^{\mathbf{2}}\mathbf{+}\mathbf{3}\mathbf{=}\mathbf{0}$

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

The equation is a quadratic equation has power of $x^2$.

So, the equation is Non-linear.

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