Differential Equations, Homogeneous equations

In summary, the conversation discusses using the method for homogeneous equations to solve the given equation. The attempt at a solution involves trying to get dx/dy on one side and substituting, but the person was not able to progress beyond that step. Another approach suggested is to substitute ##y=ux,\ dy = udx + xdu## to obtain a separable equation.
  • #1
beccajd
2
0

Homework Statement



Use the method for Homogeneous Equations to slove

(xy + y^2) dx - x^2 dy = 0

Homework Equations





The Attempt at a Solution



I attempted to get dx/dy on one side and substitute but could not get farther than this

dx/dy = x^2/(xy + y^2)
 
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  • #2
beccajd said:

Homework Statement



Use the method for Homogeneous Equations to slove

(xy + y^2) dx - x^2 dy = 0

Homework Equations





The Attempt at a Solution



I attempted to get dx/dy on one side and substitute but could not get farther than this

dx/dy = x^2/(xy + y^2)

Try ##y=ux,\ dy = udx + xdu## to get a separable equation.
 

Related to Differential Equations, Homogeneous equations

What are differential equations?

Differential equations are mathematical equations that describe the relationship between a quantity and its rate of change. They are often used to model physical systems or to predict the behavior of a system over time.

What is a homogeneous differential equation?

A homogeneous differential equation is a type of differential equation where all the terms involve only the dependent variable and its derivatives. This means that there are no explicit constants or coefficients in the equation.

How do you solve a homogeneous differential equation?

To solve a homogeneous differential equation, you can use the technique of separation of variables or the method of undetermined coefficients. Both methods involve manipulating the equation to isolate the dependent variable and then integrating to find the solution.

What is the difference between homogeneous and non-homogeneous differential equations?

The main difference between homogeneous and non-homogeneous differential equations is that non-homogeneous equations have additional terms that involve constants or coefficients. This makes them more difficult to solve compared to homogeneous equations.

What are some real-world applications of homogeneous differential equations?

Homogeneous differential equations are commonly used in physics and engineering to model systems that have a constant rate of change, such as radioactive decay or population growth. They are also used in economics and finance to model growth rates and interest rates.

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