Nonhomogeneous second order nonlinear differential equations

[Elmira1]

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

 

[drvrm]

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

 

[Elmira1]

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!

 

[the_wolfman]

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 $y'' + y' f\left(y\right) + g\left(y\right) = h\left(x\right)$ where f and g both depend on y, or is it a linear equation of the form $y'' + y' f\left(x\right) + g\left(x\right) = h\left(x\right)$ where f and g depend on x?

 

[wrobel]

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