Does anyone know how to find the equilibria for these systems of equations?

dx/dt = x3-x-y) ; dy/dt = y((2-x)/(3-y)). i've tried so many ways but none of the answers i get seem to match the answers given by our russian professor who i don't understand. the answers he got were: (0,0), (0,3), (6,0), (3/2, 3/2), can someone please explain how he got them? thanks

Answers:
Equilibrium occurs when neither of the systems is changing, i.e. when both of the differential equations are equal to 0.

Solve

     x ( 3 - x - y ) = 0
     y ( 2 - x ) / ( 3 - y ) = 0

From the second equation y = 0 or x = 2. Substitute into the first. When y = 0

     x ( 3 - x ) = 0

with solutions x = 0 or x = 3.

When x = 2

     2 ( 1 - y ) = 0

with solution y = 1.

Equilibrium points are (0,0), (3,0) and (2,1).

Did you copy down the wrong equations?
  • In indoor type transformer what type of oil is used?
  • When I Drop a glass?
  • is someone who enjoys photographing nature and insects a geek, nerd or trainspotter?
  • Is it true the United States of America uses approximately one quarter of all the fuel .?
  • why when you yawn, someone else does?
  • What does KIC stand for in metallurgy?
  • what are the characteristics that are passed from a parent to thier natural child?
  • Is evolutionary theory falsifible?