Nonhomogeneous second order nonlinear differential equations

In summary, your equation is a nonlinear equation which depends on the form of f(y), g(y), and h(x). There are a variety of analytical and numerical techniques that can help you find an exact or approximate solution. However, the choice of which techniques to try depends on the form of f, g, and h.
  • #1
Elmira1
2
0
Member warned about posting a question so scant on details
Hello every one,
I have an equation related to my research. I wonder if anyone has any suggestion about solving it?
y''+y' f(y)+g(y)=h(x)

thanks
 
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  • #2
Elmira1 said:
I have an equation related to my research. I wonder if anyone has any suggestion about solving it?

you may look up
http://www.math.psu.edu/tseng/class/Math251/Notes-2nd%20order%20ODE%20pt2.pdf
 
  • #3
drvrm said:
you may look up
http://www.math.psu.edu/tseng/class/Math251/Notes-2nd%20order%20ODE%20pt2.pdf

Thank you but my case is with non constant coefficient!
 
  • #4
Elmira1 said:
Hello every one,
I have an equation related to my research. I wonder if anyone has any suggestion about solving it?
y''+y' f(y)+g(y)=h(x)

thanks

Can you give us more details about your equation. What you have written is a very general 2nd order nonlinear equation. The solution (if one exists) strongly depends on the form of f(y), g(y), and h(x). There are numerous analytical and numerical techniques that can help you find an exact or approximate solution. However, some techniques will work better than others, and the choice of which techniques to try strongly depends of f, g, and h.

Also is your equation really the nonlinear equation [itex] y'' + y' f\left(y\right) + g\left(y\right) = h\left(x\right)[/itex] where f and g both depend on y, or is it a linear equation of the form [itex] y'' + y' f\left(x\right) + g\left(x\right) = h\left(x\right)[/itex] where f and g depend on x?
 
  • #5
Elmira1 said:
have an equation related to my research. I wonder if anyone has any suggestion about solving it?
y''+y' f(y)+g(y)=h(x)

there is no sense to speak "nonhomogeneous" about a nonlinear equation. Generally, such a type equation is not integrated explicitly. So it remains qualitative analysis or numerical analysis depending on what exactly you need from this equation
 

Related to Nonhomogeneous second order nonlinear differential equations

1. What is a nonhomogeneous second order nonlinear differential equation?

A nonhomogeneous second order nonlinear differential equation is an equation that involves a second derivative of a function, as well as nonlinear terms and a non-zero constant term. This type of equation is used to model various physical phenomena in fields such as physics, engineering, and economics.

2. How is a nonhomogeneous second order nonlinear differential equation different from a homogeneous one?

A homogeneous differential equation does not have a constant term, meaning that the right-hand side of the equation is equal to zero. In contrast, a nonhomogeneous equation has a non-zero constant term, which makes it more difficult to solve and often requires the use of numerical methods.

3. What makes a second order differential equation nonlinear?

A differential equation is considered nonlinear if the dependent variable (usually denoted by y) and its derivatives appear in nonlinear terms. This means that the equation cannot be written in the form of y'' + p(x)y' + q(x)y = f(x), where p(x) and q(x) are functions of x and f(x) is a linear function.

4. What are some real-world applications of nonhomogeneous second order nonlinear differential equations?

Nonhomogeneous second order nonlinear differential equations are commonly used to model physical systems that exhibit nonlinear behavior, such as pendulums, electrical circuits, and population dynamics. They are also used in economics to model supply and demand, and in chemistry to describe chemical reactions.

5. How are nonhomogeneous second order nonlinear differential equations solved?

There is no general method for solving nonhomogeneous second order nonlinear differential equations. In most cases, these equations are solved numerically using computer algorithms. However, in some special cases, analytical solutions can be found using techniques such as separation of variables, substitution, or power series methods.

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