Unformatted text preview: 2 cos x . (b) Write all solutions to the diﬀerential equation y = y 2 subject to the initial condition y (0) = y . Can you ﬁnd a solution that explodes at 10? And another one that explodes at 5? Can you ﬁnd a solution that explodes at x when x > 0? How does the initial condition at x = 0 connect with a speciﬁed explosion at x ? Graph one exploding solution. 4. A tissue culture grows until it has an area of 9 cm 2 . Let A ( t ) be the area of the tissue at time t . One model for the growth rate is A ( t ) = k q A ( t ) ± 9A ( t ) ² for some constant k . This is reasonable because the number of cells on the edge is proportional to q A ( t ) and most of the growth occurs on the edge. (a) Without solving the equation, show that the maximum rate of growth occurs at any time when A ( t ) = 3 cm 2 . (b) Assume that k = 6. Find the solution corresponding to A (0) = 1 and sketch its graph. (c) Do the same for A (0) = 4....
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 Spring '11
 SOSA
 Topology, Derivative, Graph of a function

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