First Order Homogeneous Differential Equations

Tutoring on First Order Homogeneous Differential Equations

Learning Objectives:

Understand and apply First Order Homogeneous Differential Equations

Math Tutoring on First Order Homogeneous Differential Equations

A First-Order Differential Equation in the form  is Homogeneous if it does not depend on x and y separately, but only the ratio   or  . Homogeneous Equations are in the form:

A Differential Equation in the form  is Homogeneous if .

A First-Order Differential Equation in the form is homogeneous if M(x, y) and N(x, y) are Homogeneous Functions of the same degree.

where is any real number and the Degree of the Homogeneous Function.

Solving a First-Order Homogeneous Differential Equation:

1.    Perform substitution using   and.

2.   Solve the resulting Differential Equation using Separation of Variables.

3.    Solve the original Differential Equation in terms of x and y.

 

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Hook Questions:

1.    When a First-Order Differential Equation is became Homogeneous?

2.   What are the steps to solve a First-Order Homogeneous Differential Equation?

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