Implicit Differential Equation: dy/dx = xy - y^2

Thread starter European Sens
Start date Mar 13, 2008
Tags

Differential Differential equation Implicit

In summary, an implicit differential equation is an equation that relates variables and their derivatives without explicitly expressing them in terms of the independent variable. The process of solving it involves finding a general solution and applying initial or boundary conditions. The main difference between implicit and explicit differential equations is how the dependent variable and its derivative are expressed. The solution is represented as a curve on the xy-plane, and these equations have various real-world applications in fields such as science, engineering, and economics.

Mar 13, 2008

European Sens

If dy/dx = xy - y^2 and y(1) = 3, then y(2) is ?

Physics news on Phys.org

Mar 14, 2008

tiny-tim

Science Advisor

Homework Helper

Hi European Sens!

Write it dy/dx = y(x - y).

Does that help?

Mar 15, 2008

OrbitalPower

Can't you just start plugging stuff in?

Mar 15, 2008

tiny-tim

Science Advisor

Homework Helper

danger!

… not if it might overload the circuit! …

Mar 15, 2008

ice109

tiny-tim said:

Hi European Sens!

Write it dy/dx = y(x - y).

Does that help?

are you trying to show him how to sole this DE?

1. What is an implicit differential equation?

An implicit differential equation is an equation that relates two or more variables and their derivatives. Unlike explicit differential equations, the dependent variable and its derivative are not explicitly expressed in terms of the independent variable.

2. How do you solve an implicit differential equation?

The process of solving an implicit differential equation involves finding the general solution, which is a relation between the variables that satisfies the equation. This can be done by using various techniques such as separation of variables, substitution, or integrating factors. The solution can then be found by applying initial or boundary conditions.

3. What is the difference between an implicit and explicit differential equation?

The main difference between implicit and explicit differential equations is the way the dependent variable and its derivative are expressed. In an implicit equation, the dependent variable and its derivative are not explicitly stated, while in an explicit equation, both are explicitly expressed in terms of the independent variable.

4. How is the solution of an implicit differential equation represented?

The solution of an implicit differential equation is typically represented as a curve in the xy-plane, where x and y are the independent and dependent variables respectively. The equation represents the relationship between the slope of the curve at any point and the coordinates of that point.

5. What are some real-world applications of implicit differential equations?

Implicit differential equations are commonly used in various fields of science and engineering, such as physics, chemistry, biology, and economics. They can be used to model complex systems and phenomena, including population growth, chemical reactions, and heat transfer. They are also essential in fields such as control theory and optimization, where they are used to design and analyze systems and processes.