1st order, non linear, homogeneous, ODE

In summary, the conversation discusses solving a given ODE with variables u and x using methods such as v-substitution and integration factor. The problem is identified as being homogeneous and non-linear, and there is some confusion about how to approach it. Some attempts at solutions are discussed, including one involving rewriting the ODE in a different form. The conversation ends with a mention of the difficulty of the class and the speaker's lack of confidence in their skills in differential equations.
  • #1
Schmoozer
30
0

Homework Statement



"Solve the following ODE's:"
"3u+(u+x)u'=0"

This is our first weeks homework and he went this through this so quickly in class.

Homework Equations



None. x and u are both variables.

The Attempt at a Solution


I know it is homogeneous and non linear. I tried v-substitution and just couldn't get a v to fit. Do i need to use the method of integration factor?

Thanks guys!
 
Last edited:
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  • #2
Schmoozer said:
I tried v-substitution and just couldn't get a v to fit.
Why doesn't this work? What do you understand by v-substitution?
 
  • #3
Not much, I feel like I'm guessing... any suggestions what i should substitute?
 
  • #4
Schmoozer said:

Homework Statement



"Solve the following ODE's:"
"3u+(u+x)u'=0"
Perhaps better to rewrite it as
[tex]u'= \frac{-3u}{u+x}= \frac{-3\frac{u}{x}}{\frac{u}{x}+ 1}[/tex]

This is our first weeks homework and he went this through this so quickly in class.

Homework Equations



None. x and u are both variables.

The Attempt at a Solution


I know it is homogeneous and non linear. I tried v-substitution and just couldn't get a v to fit. Do i need to use the method of integration factor?

Thanks guys!
 
  • #5
-(1/4)ln|(u/x)|=ln|x|+c ?

Thanks so much. This class is like diffy eq on steroids and wasn't very good at diffy eq.
 

FAQ: 1st order, non linear, homogeneous, ODE

1.

What is a first order, non linear, homogeneous ODE?

A first order, non linear, homogeneous ODE (ordinary differential equation) is a mathematical equation that describes the relationship between a function and its derivatives. It is a first order equation because it only involves the first derivative of the function. It is non linear because it contains non-linear terms, meaning that the function and its derivatives are raised to powers or multiplied together. It is homogeneous because all of the terms in the equation have the same degree.

2.

What is the difference between a linear and non linear ODE?

The main difference between linear and non linear ODEs is the form of the equation. In a linear ODE, the function and its derivatives are only multiplied by constants, while in a non linear ODE, they may be raised to powers or multiplied together. This means that the solutions to linear ODEs can often be found using algebraic methods, while non linear ODEs often require more advanced techniques such as numerical methods or series solutions.

3.

How do you solve a first order, non linear, homogeneous ODE?

Solving a first order, non linear, homogeneous ODE involves finding a function that satisfies the equation. This can be done using various techniques such as separation of variables, substitution, or integrating factors. The specific method used will depend on the form of the equation and the techniques that the solver is comfortable with. In some cases, it may not be possible to find an exact solution and numerical methods may be used instead.

4.

What are some applications of first order, non linear, homogeneous ODEs?

ODEs are used in many different fields of science and engineering to model a wide range of phenomena. Non linear, homogeneous ODEs, in particular, are often used to describe systems that exhibit non-linear behavior, such as chemical reactions, population dynamics, and electrical circuits. They are also used in economics, biology, and physics to model complex systems.

5.

What are the limitations of using first order, non linear, homogeneous ODEs?

While first order, non linear, homogeneous ODEs can model many real-world systems, they do have some limitations. In some cases, the equations may be too simplified to accurately describe the behavior of the system. Additionally, finding an exact solution to a non linear ODE can be difficult or even impossible, which may require the use of numerical methods. Furthermore, ODEs only provide a mathematical description of a system and may not take into account other factors and variables that can affect the system in the real world.

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