Question

y'=y-y2微分方程怎么解

Answer 1

y'=y-y²

dy/dx=y-y²

dy/(y-y²)=dx

∫dy/[y(1-y)]=∫ dx

∫[1/y - 1/(y-1)] dy=∫ dx

ln|y| - ln|y-1|=x + C

ln|y/(y-1)|=x + C

y/(y-1)=e^(x+C)=C₁e^x

y=yC₁e^x-C₁e^x

1=C₁e^x-(C₁e^x)/y

y=C₁e^x/(C₁e^x-1)

y=e^x/(e^x+C₂)