(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This isn't really homework help, I'm just trying to see if there is a "proper" way of doing this.

Given

[tex]\frac{dx}{dt} = x - y^2[/tex]

[tex]\frac{dy}{dt} = x - 2y + x^2[/tex]

show that the system is almost linear.

2. Relevant equations

3. The attempt at a solution

[tex]\left(\begin{array}{c}x&y\end{array}\right)' = \left(\begin{array}{cc}1&0\\1&-2\end{array}\right) \left(\begin{array}{c}x&y\end{array}\right) + \left(\begin{array}{c}-y^2&x^2\end{array}\right)[/tex],

where [tex]\left(\begin{array}{c}-y^2&x^2\end{array}\right)[/tex],

is the tail.

I was taught that the way you get the tail, is just separate the parts that are not just [tex]x[/tex] or [tex]y[/tex]. But there has to be abetter, or I should saycorrectway of finding the tail. Just separating the equation seems too simple. And besides, I tried this method for:

[tex]\frac{dx}{dt} = (1 + x) \sin{y}[/tex]

[tex]\frac{dy}{dt} = 1 - x - \cos{y}[/tex]

And it didn't work.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Tail of an Almost Linear System

**Physics Forums | Science Articles, Homework Help, Discussion**