Q6RP - 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.

$\mathit{x}\frac{{\mathbf{d}}^{\mathbf{2}}\mathbf{y}}{\mathbf{d}{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}\mathbf{3}\mathit{x}\mathbf{-}\frac{\mathbf{d}\mathbf{y}}{\mathbf{d}\mathbf{x}}\mathbf{=}{\mathit{e}}^{\mathbf{3}\mathbf{x}}$

Step-by-Step Solution

Answer

⦁    The Independent variable is x.

⦁    The dependent variable is y.

⦁    The equation is Linear.

Identifying the dependent and independent variables

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

Determining whether the equation is linear or nonlinear

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

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