Question

请问dP/dt= -aP*ln(P/b)这个怎么求积...

Answer 1

dP/dt= -aP*ln(P/b),

所以

1/b *dP/dt= -aP/b *ln(P/b),

即d(P/b)/dt= -aP/b *ln(P/b),

故 1/(P/b) * d(P/b)= -a *ln(P/b) *dt

而显然 d[ln(P/b)] = 1/(P/b) * d(P/b),

所以d[ln(P/b)] = -a *ln(P/b) *dt

故 1/ln(P/b) * d[ln(P/b)] = -a dt

对等式两边同时积分,

得到

ln | ln(P/b) | = -at +C (C为常数)

我就不继续化简了啊