system of differential equations

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April 26th 2010, 02:03 PM
cdlegendary

system of differential equations

Consider the system of first-order differential equations:
http://homework.math.ucsb.edu/webwor...96f8087751.png

Identify the two nullclines of this system, and find the two equilibrium solution coordinates.

I found the vertical nullcline to be $0=x-y^2$ and the horizontal to be $0=x-y^2$

And I know equilibrium solutions are when both vertical and horizontal null clines are zero...but how exactly do I solve for that? Do I just set the two null clines equal to each other...? Any help is greatly appreciated!
April 27th 2010, 02:32 AM
HallsofIvy

Quote:

Originally Posted by cdlegendary

Consider the system of first-order differential equations:
http://homework.math.ucsb.edu/webwor...96f8087751.png

Identify the two nullclines of this system, and find the two equilibrium solution coordinates.

I found the vertical nullcline to be $0=x-y^2$ and the horizontal to be $0=x-y^2$

??? NO! A vertical nullcline is when dx/dt= 0 which means 1- x- y= 0. Was that a typo?

Quote:

And I know equilibrium solutions are when both vertical and horizontal null clines are zero...but how exactly do I solve for that? Do I just set the two null clines equal to each other...? Any help is greatly appreciated!

No, don't set them equal to each other, set them equal to 0! What values of x and y satisfy both 1- x- y= 0 and $x- y^2= 0$ ?
April 28th 2010, 01:37 AM
rooshidavid

Well in this differential equation the method of 3rd rule chain method can be applied. Also you can use method in the form du/dv