DEhwk1_3 - Problem 1: = —y — Sm[xj Note that if you...

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Unformatted text preview: Problem 1: = —y — Sm[xj Note that if you want to generate the plcture's solutlon curve, you can use DSolve With an mitlal condition of, say y(0):1."3 Ij3'3'1‘«"e|:{1f"[x]== -Y[x] ~Sin[x]: Y[01== 1/3}: fix]. x] Hype] —> 2e“ (—1+3 ex Cos{x} m3ex SinEx1)}} tnmz: Show I: VectorPlot[{1, —y — Sin[x] } , {XI «3. 3}: {Yr —3, 3}, FrameLabel w) {x, y} , Axes n) True, VectorScale -> {Small, Tiny, None}, VectorStyle ~> Gray, StreamPoints —> Automatic, StreamStylee {Blue, Thick, “Line"}, StreamScale —-> Full, PlotLabel -> “Problem 1" I, 1 910:4E ca“x ("1+ 3 ca" Cos[x] —3 ex Sin[x]), {x, —3, 3}, PlotStylea {Black, Thick}] 013:; 31:: 33/13 mi) Lg ME“ :2 ’L giskwg Mix-F235 "Kg/“(33 B3} 59 f I” lthJ app kw], Lm; 1&5“an [k (,mgfibé agar}; * J XV!’ fig-i; "KWQJ Eng '3 “a {wkmwxflw {M‘x § E ~ ‘>< _._..—~* 3 R 3 fix ma: {(3%} 5 ’Xéfi} 3 30 hawk f a? "" “>223” “HR; 3 >04! }/\“ {A 2 I ChISec3HWK.nb Problem 26: 1—? = 0.0225*P — 0.0003 * P2 To estimate when the population is 50, plot a line P=50 (red dashed line). Show[ VectorPlot{{l, 0.0225*P — 0.0003 *PAZ}, {t, -1, 100}, {P, 0, 60}, FrameLabel —> {t, P}, Axes -+ True, VectorScale—a {Small, Tiny, None}, VectorStyle we» Gray, StreamPoints —+ {{0, 25}}, StreamStyle ~> {Blue-1, Thick, "Line"}, StreamScale —> Full, PlotLabel a “The Deer Problem“ . Plot[50, {t, ml, 100}, PlotStylea {Red, Thick, Dashed}] The Deer Problem rIfi—l_' 7"""'["""’I """"I"""T' ""Ivfilfirl—“r—Ii’j'“ ‘1 l" ' '1 '_"|__1—|__: ChISec3HWK.nb | 3 Here, we need to see what value the population tends to...ex£end the direction field. It looks like we're heading towards 13:75. Test this by plotting P=75. I‘ve also added another solution curve to show that if the populatino is above or below P=75, the population always converges to P275. (One exception: P=D). Show[ VectorPlot[{l, 0.0225*P — 0.0003*P*2} , {t, —1, 300}, {P, 0, 160}. FrameLabel —> {t, P}, Axes —> True, VectorScale -> {Small, Tiny, None}, VectorStyle —-> Gray, StreamPoints we {{0, 25}, {0, 150}}, StreamStyle —> {Blue, Thick, "Line"}, StreamScale —> Full, PlotLabel «a "The Deer Problem", Plot[50, {t, —1, 100}, PlotStylew) {Red, Thick, Dashed}], Plot[75, {t, ml, 300}, PlotStyle —) {Darker[Green} , Thick, Dashed}] Tile Deer Problem g“! "-1 - r”! "i l i' = 'v 'r 'r' ; "J'Tmr 'T";"I’”l"t""’]" f'T‘r—tililil—T’T’T‘r’ P ‘_.._! z i L- l i r i_l l i i i i L_- - cl 1 i_l_1._. L....__..._.l_..il.....l....ilj U 50 100 150 100 250 300 ...
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DEhwk1_3 - Problem 1: = —y — Sm[xj Note that if you...

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