请问dP/dt=-aP*ln(P/b)这个怎么求积...RT,dP/dt=-aP*ln(P/b),a和b都是常数.

Question

请问dP/dt= -aP*ln(P/b)这个怎么求积...
RT,dP/dt= -aP*ln(P/b),a和b都是常数.

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[...