Understanding Differential Equations

The video tutorial explains how to determine the order and linearity of differential equations. It defines the order as the highest derivative present and describes linear equations as those fitting a specific form. Through examples, it illustrates how to identify linear and nonlinear equations based on their terms. The tutorial covers four examples, highlighting the characteristics that make an equation linear or nonlinear.

What determines the order of a differential equation?

• The number of terms in the equation

• The highest derivative present

• The highest power of the variable

• The number of constants in the equation

Which of the following forms represents a linear differential equation?

• f(T, y, y^2) = 0

• f(T, y, y') = 0

• f(T, y^2, y') = 0

• f(T, y', y'') = 0

In the equation 'cos(T) * y''' = 5y', what is the order of the differential equation?

• Two

• Four

• Three

• One

Why is the equation '5y' - 2y^2 = 0' considered nonlinear?

• It contains a y^2 term

• It includes a derivative

• It has a constant term

• It has a function of T

Which term in a differential equation makes it nonlinear?

• A term with a constant

• A term with a derivative

• A term with y

• A term with y^2

What is the order of the equation 'y''' = sin(T + y)'?

• Three

• One

• Four

• Two

Why is 'y''' = sin(T + y)' considered nonlinear?

• It has a constant term

• It contains a function of T + y

• It includes a function of T

• It has a derivative term

In the equation 'y'''' - T * y'' + 4y = 1', what is the order?

• Two

• Four

• One

• Three

Which of the following is true for a linear differential equation?

• It can have a y' term

• It can have a constant term

• It can have a y'' term

• It can have a y^2 term

What makes the equation 'y'''' - T * y'' + 4y = 1' linear?

• It has a function of T + y

• It fits the form of a linear equation

• It has a constant term

• It has a y^2 term