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4. Autonnomous equations:

Sec 1.6: Autonomous equations Determine which differential equation corresponds to each phase diagram. You should be able to
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X f (2) [Autonomous equation] fixed points are determined by f(x) = o. if x* is a fixed point Thent phase diagram I Reason f(dx - -3x = x(x-3) dt fixed points are ²-3x=0 x=0,3. f(ots) - 5 (8-3) co Esro 8-340 & is someall a number. f(0-8)= -8 (-8-3))fixed points are. x=0,2 f(ot) = 8(8-2) to f(0-) = -5(-8-2) >0 ) of (2+8) = (2+8) 8 7 0 7 ore @ 4 x - x - 42 = 2(x-2)(x+2) fix7. dx 2(2-)? dt fixed points x=0,2 +(ot) yo f (2+) >0 flo-) <0 ) f (2-) > 0 + - 6 (at) (6) ©.2. doe - 4x = *} = 7(2-4) (2 + x

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4. Autonnomous equations: Sec 1.6: Autonomous equations Determine which differential equation corresponds to each phase diagram....
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