How do I convert a complicated differential equation into autonomous form?

[thecoop]

hi guys , i want to write a complicated differential equation as autonomous equations , is there any method ? i have no idea to overcome it !



thank you

 

[voko]

It may be possible to introduce a new variable, which will eliminate the time from the equation. For example:

(x' - x)t + x = 0

Let u = xt and the equation becomes

u' = u

If that fails, you can always convert an equation to an autonomous system of two equations in two variables, letting the second variable = time.