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Math · Advanced Math
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QUESTION 1 Consider the equation iksgn) +csgn(r) 0, (c> k) (a) Determine the equilibrium point (b) By letting dy 1 d in the equation, deduce the function h(r), such that h)+ C describes the phase paths, where C is an integration constant. (c) Determine the path starting at (ro.0) in the fourth quadrant. That is, in the quad- rant described by r > 0.y<0. (6) Use continuity of the path into <0,y < 0 to deterine the path in the thir quadrant (ii) Use continuity of the path into z < 0,y > 0 to determine the path in the second quadrant. r1

20 (ii) Use continuity of the path into z>O,y>0 to determine the path in the first quadrant. termine a point on the positive r axis where the path cuts. (e) Finally, sketch the phase diagrams. 20

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