DEhwk2_2 - 552.1wa4 J6) I‘lej W { \ af-ffi. L a ‘5}...

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Unformatted text preview: 552.1wa4 J6) I‘lej W { \ af-ffi. L a ‘5} if: f waw ~ (X) N: r l f f 1% \ x a §(X¥~O M imwg 5} (X A %:§Qm Ff {{r’ §0\{J qufl§\§fix;:fl M H U g “i Smi‘ifi “ W -~ 3 ~» ~ 73 M: Wm M “.3 = SEEM? mi” 7 t 1’: Emmy ‘ ' Ci H.311- EH 1“": “m QGL % EC fix: “ ‘39:”,“4”323:1] J Cy 6 ' I 2‘ -’ -.—-._ ,,,, WV 77 ‘m' m g “K 3“ “fif%:fi“:f E‘” 4% M m m w m m 01 m ‘ w_._g,‘,,,r O f": Whom K m _. L ,,. ,. “RAM; : {13x(\0~">43w\"\‘> “Vi W‘X'i‘gok O 1 M ,X m ir i um - Link '0‘: W23“ @520 M m 'g aka—wk Mr”; "M a. “’2'” m {x : ‘5 "t me ) 1:3» ‘3 * SJ: awe?“ f Sm} 25m MEm‘i ismtsmfl 19> M” “3;; "" 523 d ‘ “W a: Problem 6: How to solve it directly... :3.» DSolvehc ' [1:] == 9 — x[t] *xEt] , x[t] , t] 3 (E61: _escu§) {KNEE {{x[t] _3 2| Ch25£c2HMflCnb Problem 17 130111135"= {{Or 1}; {0: 3}; {0r 4-}, {0: -3}}; f[x___] :=x‘2*(x‘2-4); (1" To find the critical numbers: (Note repeated roots) 9:) critNumb = x / . Solve [f[x] == 0 , x} Show[ VectorPlot[{1, f[x] } , {t, -0.1, 2}, {x, —5, 5} , FrameLabel -) {t, x} , Axes —) True, VectorScale -> {Tiny, Tiny, None} , VectorStyle —> Gray, StreamPoints —) Automatic , Streamstyle —> {9urple, Thick, "Line"} , StreamScale a Full , (* Generates solid curves for sample solutions *) PlotLabel —> "Direction Field" , Epiloga {PointSize[Large] , Point[points}} (*- A good way to indicate the initial conditions 9:) I (a: Note that the color Brown doesn't appear because it is one of the repeated roots. . .and Red is placed on top of it. *) Plot[critNumb, ft, —0. 1, 2}, PlotStyle —+ {{Blue, Thick}, {Brown, Thick}, {Red, Thick}, {Green, Thick}}] CREE—’17]: [*2, D, 0, 2] inaction Field 1'1" .‘1'1'. L Y"'""IWT'M'"IHMTW‘MIW”YW‘“"“‘t""’*l+ L.) t WLMWL.WL_._.J NJ. ChzseczHWK.nb | 3 Problem 19 (n Inffl]: sols =x/. Solve[l/10*x* (lD—x) —h= 0, x] Omani: {ES—H‘JS—Eh, 5+V5—V5—2h} |n[5:3]:= Plot[sols, {h, —3, 3}, PlotStyle a {{Blue, Thick}, {Red, Thick}}, AxesLabel —> {11, x}} Oui[53}= ...
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DEhwk2_2 - 552.1wa4 J6) I‘lej W { \ af-ffi. L a ‘5}...

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