Chapter 1.6 Autonomous Equilibrium Solutions and Substitution .pdf

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University at Buffalo*
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MTH 306
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Feb 10, 2024
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Examplea : X = - 5 -x)2 Phase Diagram (unstable) 0 = - 6(X - 2) X = b 5 - X = 0 d = - (5 - 3)2 5 - 1 x = 5 eq soln . (negative) X = 0 dx = - (0 - 5)2 dt x = - 25 (negative) Example 3 : = - S(X - 2) x 10) = x o dx = - S(X - 2) dt 1 dx = bt - (5 - x)2 u = S - X f( (5 - x)"dx = fdt du = - 1dx Su du = = 1 = t + C T - 1 = t + C - S + x x - 5 = 5 - X $ 1 1 t + C I - (5 - x) = t + C X = t + c + 5
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