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: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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- Spring '11
- KeithEmmert
- How to Solve It, Ci H.311- EH, §Qm Ff, X¥~O M imwg, MEm‘i ismtsmﬂ