dy/dx=y(1-y)如何求解

题目详情

dy/dx=y(1-y)如何求解

▼优质解答

答案和解析

dy/dx=y(1-y)
dy/[y(1-y)]=dx
[1/y+1/(1-y)]dy=dx
两边积分得
lny-ln(1-y)=x+C1
ln[y/(1-y)]=x+C1
y/(1-y)=e^c1e^x=Ce^x

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