Advanced ENGINEERING MATHEMATICS 6판 공업수학 솔루션
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2.1 Solution Curves Without the Solution
15. (a) The isoclines have the form y = −x + c, which are straight lines with slope −1.
(b) The isoclines have the form x2 + y2 = c, which are circles centered at the origin.
16. (a) When x = 0ory = 4,dy/dx =−2sothelinealelementshaveslope−2. When y = 3ory = 5,dy/dx = x−2, so the lineal elements at (x,3) and (x,5) have slopes x−2.
(b) At (0,y0) the solution curve is headed down. If y →∞as x increases, the graph must eventually turn around and head up, but while heading up it can never cross y = 4 where a tangent line to a solution curve must have slope −2. Thus, y cannot approach ∞ as x approaches ∞.
17. When y<1 2x2, y = x2 − 2y is positive and the portions of solution curves “outside” the nullcline parabola are increasing. When y>1 2x2, y = x2−2y is negative and the portions of the solution curves “inside” the nullcline parabola are decreasing.
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Chapt_14.pdf
Chapt_15.pdf
Chapt_16.pdf
Chapt_17.pdf
Chapt_18.pdf
Chapt_19.pdf
Chapt_20.pdf
Chap+1.pdf
Chap+2.pdf
Chap+3.pdf
Chap+4.pdf
Chap+5.pdf
Chapt_01.pdf
Chapt_02.pdf
Chapt_03.pdf
Chapt_04.pdf
Chapt_05.pdf
Chapt_06.pdf
Chapt_07.pdf
Chapt_08.pdf
Chapt_09_1.pdf
Chapt_09_2.pdf
Chapt_10.pdf
Chapt_11.pdf
Chapt_12.pdf
Chapt_13.pdf
