• Support PF! Buy your school textbooks, materials and every day products Here!

Find the type of equilibrium at (0,0) for x'=x, y'=y

  • Thread starter anicic
  • Start date
  • #1
1
0

Homework Statement



I need to solve the differential equations given, find the type and stability of the equilibrium at (0,0), without matricies.

Homework Equations



none

The Attempt at a Solution



starting:

x' = x
y' = y

dy/dx = y'/x' = y/x

=> dy/y = dx/x

integrating gives

ln y + c1 = lnx + c2

rearrange and get

ln(y/x) = c


have i done it right so far?
i get stuck at this point
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,793
922
I'm only wondering why you are solving for y as a function of x at all.

dx/dt= x, dy/dt= y. What is true about the derivatives if x and y both close to 0 but positive?
 

Related Threads for: Find the type of equilibrium at (0,0) for x'=x, y'=y

Replies
1
Views
1K
  • Last Post
Replies
5
Views
12K
Replies
3
Views
664
  • Last Post
Replies
8
Views
1K
Replies
3
Views
389
Replies
9
Views
617
Replies
6
Views
11K
Replies
11
Views
678
Top