Please explain only the yellow circled part. Where are theformula and the numbers in this section come from. Please donot redo the question. Only do the yellow circled part.
Please Explain Only The Yellow Circled Part Where Are The Formula And The Numbers In This Section Come From Please D 1 (142.63 KiB) Viewed 8 times
Question 6 second order non-linear differential equation: Classify the critical points of the plane autonomous system corresponding to the [10 marks] = Solution Let y✓then y −x+v(1-x²)y√. For the critical points : x = 0 =ý⇒x= x= 0 so x = 0. Therefore the critical point is (0,0)✓. Jacobian is J J(0,0) = (-1₁) ✓ ï+v(x² − 1)x + x = 0. ν> 2: 1 0 -1-2xyv v(1- x²) 2²2)) ✓ T = V ⇒T> 0 (Unstable) and T < 0(Stable) Δ=1 7² − 4A = v² − 4 = (v − 2)(v + 2)√ ⇒ −2 < v < 2 ⇒ 7² − 4 < 0 (Spiral) ν>2 ⇒ 7² − 4 > Onode v < -2 Unstable node✓
0 <v <2: Unstable Spiral✓ -2 <v < 0: stable Spiral✓ v < -2: stable node✓ v = 2: degenerate unstable node. v=-2: degenerate stable node.
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