Help to reduce solution of differential equation: dy/dx=(xy+y)/(x+xy)

Thread starter Queren Suriano
Start date Jun 17, 2019
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Differential Differential calculus Differential equation

In summary, differential equations are solved by separating variables, integrating both sides, and solving for the constant of integration. The notation dy/dx in a differential equation represents the rate of change of y with respect to x. Techniques such as substitution and separation of variables can be used to reduce the solution of a differential equation, making it easier to work with and providing insight into the system's behavior. Real-life applications of differential equations include modeling and analyzing systems in various fields, such as physics, engineering, economics, and biology.

Jun 17, 2019

Queren Suriano

Homework Statement: I have found this solution but I would like to solve for "Y" to write its general solution.

ln(y) +y = ln(x) + x +C

Relevant Equations: ln(y) +y = ln(x) + x +C
y=?

ln(y) +y = ln(x) + x +C
y=?

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Jun 17, 2019

fresh_42

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You will need Lambert's W-function for it, or go for some local solutions.

FAQ: Help to reduce solution of differential equation: dy/dx=(xy+y)/(x+xy)

1. What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves the use of derivatives, which represent the rate of change of the function, to model real-world phenomena.

2. Why is it important to reduce a solution of a differential equation?

Reducing a solution of a differential equation simplifies the equation and makes it easier to analyze and solve. It also helps to identify the behavior of the function and its derivatives, which can provide insights into the underlying system or process being modeled.

3. What is the process for reducing a solution of a differential equation?

The process for reducing a solution of a differential equation involves manipulating the equation algebraically to isolate the dependent variable and its derivatives on one side of the equation, and all other terms on the other side. This can involve techniques such as separation of variables, integration, and substitution.

4. How can reducing a solution of a differential equation help in practical applications?

In practical applications, reducing a solution of a differential equation can help to make predictions and solve problems related to the system or process being modeled. It can also provide insights into the behavior of the system or process, which can aid in decision-making and problem-solving.

5. Are there any limitations to reducing a solution of a differential equation?

Yes, there are limitations to reducing a solution of a differential equation. In some cases, it may not be possible to find an exact solution, and approximations or numerical methods may be needed. Additionally, the assumptions and simplifications made during the reduction process may not accurately reflect the real-world system or process being modeled.