lecture_7 (dragged) 2 - y = G ( t, y ). Then the limiting...

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MA 36600 LECTURE NOTES: WEDNESDAY, JANUARY 28 3 for some function f ( y ). We have seen several examples of autonomous equations: If v = v ( t ) denotes the velocity at time t of an mass m falling under the inFuences of gravity and air resistance, then dv dt = g γ m v for some constant γ .I f P = P ( t ) denotes the size of a population at time t ,then dP dt = rP ° 1 P K ± for some constants r and K . We may also consider di±erential equations in the form dy dt = y n ,n ° =0 , 1; such equations are called Bernoulli equations . (In Lecture 7, we worked out an example with n =1 / 3.) Say that y = y ( t ) is a solution to the di±erential equation
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Unformatted text preview: y = G ( t, y ). Then the limiting value y L = lim t y ( t ) is an equilibrium solution. In fact, all equilibrium solutions can be found by nding constants y L such that G ( t, y L ) = 0 for all time t . Equilibrium solutions are easy to nd for autonomous equations: If G ( t, y ) = f ( y ) is independent of time, then an equilibrium solution satises f ( y L ) = 0 . Such solutions y L are called critical points for the function f ( y )....
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This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue University-West Lafayette.

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