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求微分方程dy=ky(N-y)dx (N,k>0 为常数)的解?
人气:173 ℃ 时间:2020-05-25 11:18:50
解答
由已知有
dy/(ky(N-y)) = dx
两边积分有
∫dy/(ky(N-y)) = x
左边那个积分= (1/k)∫dy/(y(N-y)) = (1/(kN))(∫dy/y + ∫dy/(N-y))
=ln|y/(N-y)|/(kN)+C
所以有 (y/(N-y))^(1/(kN)) =Cx
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