Question

Answer Problems 1-12without referring back to the text. Fill in the blanks or answer true or false.

An example of a nonlinear third-order differential equation in normal form is.

Short answer

$\frac{d^{3}y}{d{x}^3}=\tan \left(xy\right)$

Step-by-step solution

Definition

The standard form of a linear differential equation is$\frac{\mathbf{d}\mathbf{y}}{\mathbf{d}\mathbf{x}}\mathbf{+}\mathit{P}\mathit{y}\mathbf{+}\mathit{Q}$, and it contains the variable y, and its derivatives.

Function

The trigonometric function makes the differential equation nonlinear, since theterm is in the trigonometric function.

$\frac{d^{3}y}{d{x}^3}=\tan \left(xy\right)$

The third derivative means the differential equation is third-order.