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7.An island is inhabited by two species of animals, A and B .Let x and y be
respectively the populations of A and B at time t. Assume that x and y can be treated
as continuous variables. The rates of change of x and y are directly proportional to
x+y and x-y respectively, with proportionality constants of unity(in suitable units )in
both cases .At time t=0, the populations of A and B are both N.
(a)show that dy/dx=x-y/x+y (3 marks)
(b)By solving the equation in (a),show that x and y satisfy the relation
x^2-2xy-y^2+2N^2=0
我想問b part..我做到
-1/2 ln | (x^2-2xy-y^2)/x^2| = ln|x| - 1/2ln2 - lnN
ln | (x^2-2xy-y^2)/x^2| = ln2 + 2lnN - 2ln|x|
(x^2-2xy-y^2)/x^2 = 2N^2 / x^2
x^2-2xy-y^2 - 2N^2 = 0 ...
個2N^2 係負 =.= |
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