Solution: 715 A system of differential equations is given. (a) Construct the phase

Chapter 7, Problem 7

(choose chapter or problem)

715 A system of differential equations is given. (a) Construct the phase plane, plotting all nullclines, labeling all equilibria, and indicating the direction of motion. (b) Obtain an expression for each equilibrium. 7. x9 xs3 2 x 2 yd, y9 ys2 2 x 2 yd, x, y > 0 8. p9 ps1 2 p 2 qd, q9 qs2 2 3p 2 qd, p, q > 0 9. n9 ns1 2 2md, m9 ms2 2 2n 2 md, n, m > 0 10. x9 xs2 2 xd, y9 ys3 2 yd 11. p9 2p2 1 q 2 1, q9 qs2 2 p 2 qd 12. p9 2q 2 1, q9 q2 2 q 2 p 13. x9 5 2 2x 2 xy, y9 xy 2 y, x, y > 0 14. z9 z 3 2 4z 2 1 3z 2 2w, w9 z 2 w 2 1 15. x9 2sx 2 2d lnsxyd, y9 ex sx 2 yd, x, y . 0

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