# Program 02b: The logistic equation; example 4-ch2.
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from sympy import dsolve, Eq, Function, symbols, pprint
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t, b, d = symbols('t beta sigma')
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P = symbols('P', cls=Function)
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dPdt = P(t).diff(t)
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de = Eq(dPdt, P(t)*(b-d*P(t)))
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print('program 02b:\n')
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pprint(de)
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sol = dsolve(de, P(t))
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pprint(sol)
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