Linear and Non-linear Differential Equations

This video tutorial from NumberX introduces the concepts of linear and non-linear differential equations. It explains the properties that define a linear differential equation, such as the degree and exponent of differential quotients and dependent variables. The tutorial also covers how to identify non-linear differential equations by providing examples that do not meet the criteria for linearity. The video concludes with a prompt to subscribe for more educational content.

What is the main topic of the lecture?

• Linear and Non-linear Differential Equations

• Quadratic Equations

• Integral Calculus

• Probability Theory

Which of the following is a characteristic of a linear differential equation?

• Exponent of each differential quotient is two

• Degree of DE is greater than one

• Contains product of y and dy/dx

• Degree of DE is equal to one

What is the exponent of each dependent variable in a linear differential equation?

• Three

• Two

• One

• Zero

Which of the following is NOT a property of a linear differential equation?

• Exponent of each differential quotient is one

• Degree of DE is equal to one

• Exponent of each dependent variable is one

• Contains product of y and dy/dx

What is the degree of a linear differential equation?

• Zero

• One

• Two

• Three

Which term is not allowed on the left-hand side of a linear differential equation?

• Sum of y and dy/dx

• Difference of y and dy/dx

• Quotient of y and dy/dx

• Product of y and dy/dx

What is the exponent of each differential quotient in a linear differential equation?

• Zero

• One

• Two

• Three

In the equation dy/dx + f(x) * y = g(x), why is it considered linear?

• It satisfies all properties of a linear differential equation

• It contains a product of y and dy/dx

• It has a non-linear term

• It has a degree of two

What happens if a differential equation does not satisfy the four properties of linearity?

• It becomes a quadratic equation

• It is considered a non-linear differential equation

• It becomes a polynomial equation

• It is considered a linear differential equation

Which of the following is an example of a non-linear differential equation?

• dy/dx = y^2 + x

• dy/dx + f(x) * y = g(x)

• dy/dx = f(x)

• dy/dx = y + x