Question

Consider the given system di = 2x²y – 3x2 - 25 y, y=-2xy? + bxy. x Incorrect (a) Determine all critical points of the given system of equations. Write your points in ascending order of their x-coordinates: if two points have the same x-coordinate, write them in ascending order of (x2.72) =( x Incorrect. (b) Find the corresponding linear system near each critical point. 1. The linear system near the critical point ($1.91) () = A (s) where: 1. The linear system near the critical point (*1. ) AL = Select for Adobe Flash

Answer 1

@hse- re he py- & dx = 0 = dy fer equilibrum put by © & & a=(e+ h-) Pixe a&th-so offres Xy so of 933 &x=0 or y=0 ay=3 Шам хео by D dx = 2x²y - 3x²-25y = 0 -259-0 By=0 (x, y) = 10,0) al when y=0 - 3x² -0 & X=0 CO) when de x y=3 - 3x2 - 75=0

3 x 2 = 75 x²= 25 x=+5) equilibrum pet (5,3 and 1-5,3) (a, ,Y)= (0,0) (12, Y) = (5,3) (X3, Zz) = (-5,3 6 6 linear ut system filx,y) = 2x²y - 3x² -25 y fə (x, y) = -2x y² + bay J (x,y) = (at the Jacobian I Enly) - [txy -6x 2x²257 L-ay?t by - xy + x Near Coo 1- To

Near (5,3) J15, 3) = [ 30 25 Near (-5,3) 3153) 130 30 eigenvalue for 710,0) = 10 -25] 1x=0,₂ =0) eigenvalue foe J15,3) - [ 30 257 0 -30 (x, = -30 10 30 fer 1153) [13 ] LA -30 = 30)