# Asymptotic solution to a differential equation

1. May 8, 2006

### eljose

if we have the equation:

$$y^{n}= F(y, \dot y, \ddot y, \dddot y,...........,y^{n-1} )$$

where F can be a very difficult expression in the sense that can be non-linear and so on..my question is ¿how could we get an asimptotyc solution
y(x) with x--->oo of the differential equation...thanks.

2. May 8, 2006

### anton

Last edited by a moderator: Apr 22, 2017
3. May 13, 2006

### eljose

and there is no form to know how the differential equation diverges?..for example let,s suppose that for big x $$y(x) \sim x^{a}$$ where a is a real and positive exponent then my question is if there would be any way to calculate a..thank you.

4. May 13, 2006

### Clausius2

There's no general method for working out the asymptotic behavior of non linear differential equations. When it is non linear you're on your own. We usually assume a dominant balance and afterwards check it out, or we assume a behavior as you did. Your "a" can be calculated substituting your expression (if suitable) in the differential equation.