Differential Equations: Definitions and Terminology (Level 3 of 4)

The video tutorial explains how to classify Ordinary Differential Equations (ODEs) by order and linearity. It provides examples of different ODEs, demonstrating how to identify the dependent and independent variables, determine the order by identifying the highest derivative, and assess linearity by checking if the dependent variable and its derivatives are linear and expressed in terms of the independent variable. The video covers examples of third-order linear, second-order linear, second-order nonlinear, first-order nonlinear, and second-order linear ODEs.

What is the highest order derivative in the first example discussed?

• First derivative

• Second derivative

• Fourth derivative

• Third derivative

In the first example, what type of functions are used to express the products of the dependent variable and its derivatives?

• Polynomial functions

• Logarithmic functions

• Trigonometric functions

• Exponential functions

What is the order of the ODE in the second example?

• Second-order

• First-order

• Third-order

• Fourth-order

Which of the following is NOT a transcendental function mentioned in the second example?

• Exponential function

• Trigonometric function

• Natural logarithm

• Polynomial function

In the third example, why is the ODE classified as nonlinear?

• The equation contains a constant

• The independent variable is not time

• The dependent variable is inside a transcendental function

• The derivative is raised to a power greater than 1

What is the order of the ODE in the fourth example?

• Third-order

• First-order

• Fourth-order

• Second-order

In the fourth example, what makes the ODE nonlinear?

• The presence of a constant

• The absence of derivatives

• The use of trigonometric functions

• The dependent variable is raised to a negative power

What is the order of the ODE in the final example?

• Second-order

• Fourth-order

• Third-order

• First-order

In the final example, what ensures the ODE is classified as linear?

• The presence of constants

• The absence of transcendental functions

• The function E is expressed in terms of the dependent variable

• The dependent variable and its derivatives are raised to the power of 1

What would make the ODE in the final example nonlinear?

• If the function E were a constant

• If the function E were expressed in terms of Q

• If the function E were a polynomial

• If the function E were expressed in terms of t