Can Rationalizing the Denominator Solve a Stuck Homogeneous Equation?

MHB
Thread starter Joe20
Start date Feb 17, 2019
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Homogeneous Homogeneous equation

In summary, a homogeneous equation is a mathematical equation with terms of the same degree and a constant term equal to 0. It can be solved by finding values for the variables that satisfy the equation. This is important in science and engineering, and a homogeneous equation can have infinitely many solutions due to its property of scaling.

Feb 17, 2019

Joe20

Hi, I have solved this ODE till half way and got stucked on the integration of some weird expression. Need help for this.
Thank you!

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Feb 18, 2019

GJA

Gold Member

MHB

Hi Alexis87,

Rationalizing the denominator should help.

What is a homogeneous equation?

A homogeneous equation is an algebraic equation where all the terms have the same degree. This means that all the variables in the equation have the same exponent.

What is the difference between a homogeneous and non-homogeneous equation?

A non-homogeneous equation has terms with different degrees, while a homogeneous equation has terms with the same degree. In other words, a non-homogeneous equation has a constant term, while a homogeneous equation does not.

How do you solve a homogeneous equation?

To solve a homogeneous equation, you can use the substitution method or the elimination method. First, rearrange the equation so that all the terms are on one side and the other side is equal to zero. Then, substitute a variable with another variable, and solve for the remaining variable. Repeat this process until you have solved for all the variables.

Can a homogeneous equation have more than one solution?

Yes, a homogeneous equation can have infinitely many solutions. This is because when you substitute a variable with another variable, you are essentially finding a different solution for the equation.

What are the applications of solving homogeneous equations?

Solving homogeneous equations is used in various fields such as physics, engineering, and economics. It is used to model and solve problems involving proportions, mixtures, and growth rates. In physics, it is used to solve problems involving forces and motion. In economics, it is used to analyze supply and demand equations.