# Ordenary differential equation

• hhegab
In summary, the conversation discusses a specific ODE that the speaker has been unable to solve using the integration factor technique. The equation cannot be made exact and the speaker asks for help in finding a solution, possibly using an integral transform. They also mention struggling with the problem for two months and ask if the other person has any suggestions.
hhegab
Hi,
I have the following ODE, which I could not solve,
(7x^3+3x^2y+4y)dx+(4x^3+x+5y)dy=0.
I have tried to use the integration factor technique, but I could not find one.
It can be put in the form:
M dx +N dy=0, where M=7x^3+3x^2y+4y, and N=4x^3+x+5y.
Can you help me? And How can it be done on mathematica? (or MuPAD)

hhegab

I don't see any way to make this equation exact either. Were you given any initial conditions, or are you to find a general solution? The reason I ask is that, if you were, we may be able to use an integral transform.

Sorry, but I don't know how to use Mathematica.

Dear Tom,
This problem appears in my book! I have struggled with it for 2 months (and I shouldn't have done).
Well, I guess I will stop now.
PS.
It is said that it has an integration factor ! I have done my best to find it, but it was not there.

hhegab

I will wrestle with this some more over the weekend. Take a break!

## 1. What is an ordinary differential equation (ODE)?

An ordinary differential equation (ODE) is a mathematical equation that describes the relationship between a single independent variable and one or more dependent variables. It involves derivatives of the dependent variables with respect to the independent variable.

## 2. What is the difference between an ODE and a partial differential equation (PDE)?

An ordinary differential equation (ODE) involves only one independent variable, while a partial differential equation (PDE) involves multiple independent variables. ODEs are used to model systems that change over time, while PDEs are used to model systems that change over both time and space.

## 3. What is the order of an ODE?

The order of an ODE is determined by the highest derivative present in the equation. For example, a first-order ODE only involves the first derivative, while a second-order ODE involves the second derivative.

## 4. How are ODEs used in science?

ODEs are used in many scientific fields, including physics, engineering, biology, and chemistry, to model and understand the behavior of systems that change over time. They are often used to predict future outcomes and make informed decisions.

## 5. What are some common techniques for solving ODEs?

Some common techniques for solving ODEs include separation of variables, substitution, and the use of integrating factors. Numerical methods, such as Euler's method and the Runge-Kutta method, can also be used to approximate solutions to ODEs.

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