# Classify fixed points non homogeneous system of linear differential equations

## Homework Statement

$$\dot{x}=2x+5y+1, \dot{y}=-x+3y-4$$

## The Attempt at a Solution

Well, if system was: $$\dot{x}=2x+5y, \dot{y}=-x+3y$$ we let a=2, b=5, c=-1, d=3.
Then p = a + d and q =ad - bc and we investigate $$p^2-4q$$
Don't know what to do when $$\dot{x}=2x+5y+1, \dot{y}=-x+3y-4$$
Thanks

Last edited:

$$2x + 5y = -1; -x + 3y = 4;$$
for x and y. Assume we obtain the solutions $x=x_0, y=y_0$. Then a substitution of the form $x^* = x + x_0; y^* = y + y_0$ will give you a set of homogeneous ODEs in a shifted coordinate system. Fixed points of this new set of ODEs are related to the old set by the coordinate transformations above.