# MAT 127: Calculus C the solutions (x, y) = (x(t), y(t)) to the system of differential equations…

Problem E According to the effect, the disruptions (x, y) = (x(t), y(t)) to the classification of differential equations ( dx dt = ax - bxy dy dt = -cy + dxy (1) delay actual invariables a, b, c, d > 0 deduce pure barred curves (loops) in the xy-plane.

MAT 127: Calculus C, Fall 2010 Homeeffect Assignment 5 WebAssign Problems due precedently 9am, Wednesday, 10/20 (all sections) 20% boon for submissions precedently 9am, Saturday, 10/16 Written Assignment due precedently 9:35am Wednesday, 10/20 in Library E4320 if enrolled in L01 5:20pm Thursday, 10/21 in Library W4525 if enrolled in L02 2:20pm Thursday, 10/21 in Library W4540 if enrolled in L03 This height set is longer than habitual, gone it covers environing 1.5 weeks. Please interpret Sections 7.6 and 8.1 in the texteffect completely precedently starting on the identical heights underneath. Written Assignment: 7.6 2,6,8; 8.1 22,33; Problems E,F (instant page) Briey expound your counterpart on all texteffect heights and profession your effect on the communication heights Please transcribe your disruptions legibly; the graders may ignorance disruptions that are not interpretily interpretable. All disruptions must be stapled (no disquisition clips) and enjoy your spectry and exhortation calculate in the upper- proper nook of the rst page. Problem E According to the effect, the disruptions (x; y) = (x(t); y(t)) to the classification of dierential equations (dx dt = ax ?? bxy dy dt = ??cy + dxy (1) delay actual invariables a; b; c; d > 0 deduce pure barred curves (loops) in the xy-plane. Let's see why. (a) Divide the prevent equation in (1) by the rst and work-out the resulting equation obtaining y = y(x) implicitly; in doing so affect that x; y > 0 (so singly the rst quadrant is considered). (b) Fix the invariable C in your unconcealed disruption (this gives a specic disruption of the equation in (a)). Profession that the values of x; y > 0 that meet the equation lie in the gap [mC;MC] for some mC;MC > 0. Furthermore, for each xed x > 0 at most two values of y > 0 meet the equation; for each xed y > 0 at most two values of x > 0 meet the equation. Hint: Your unconcealed disruption in (a) should be of the arrange G(y) = CF(x). Profession that F =F(x) and G=G(y) enjoy certainly one momentous purpose in the gap (0;1), which is a restriction in one contingency and a climax in the other contingency. Sketch their...

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