Q3RP - 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.

${\mathbf{y}}^{\mathbf{3}}\frac{{\mathbf{d}}^{\mathbf{2}}\mathbf{x}}{{\mathbf{dy}}^{\mathbf{2}}}\mathbf{+}\mathbf{3}\mathbf{x}\mathbf{-}\frac{\mathbf{8}}{\mathbf{y}\mathbf{-}\mathbf{1}}\mathbf{=}\mathbf{0}$

Step-by-Step Solution

Answer

⦁    The Independent variable is y.

⦁    The dependent variable is x.

⦁    The equation is Linear.

Identifying the dependent and independent variables

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

Determining whether the equation is linear or nonlinear

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

Hence, the Independent variable is y. The dependent variable is x. The equation is Linear.