dW/dt=(m-n-kW)W运用积分反推成W(t)=?

题目详情

dW/dt=(m-n-kW)W
运用积分反推成W(t)=?

▼优质解答

答案和解析

dt/dw=1/(m-n-kw)w
=(1/w+k/(m-n-kw))/(m-n)
t=[ln(w)-ln(m-n-kw)]/(m-n)+C
t=ln(w/(m-n-kw))/(m-n)+C
w/(m-n-kw)=e^[(t-C)(m-n)]
从而解出w

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