求dy/dx=y(y-1)的通解

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/12 16:44:39
求dy/dx=y(y-1)的通解求dy/dx=y(y-1)的通解求dy/dx=y(y-1)的通解dy/dx=y(y-1)dy/[y(y-1)]=dx∫dy/[y(y-1)]=∫dx∫dy/(y-1)-

求dy/dx=y(y-1)的通解
求dy/dx=y(y-1)的通解

求dy/dx=y(y-1)的通解
dy/dx=y(y-1)
dy/[y(y-1)]=dx
∫dy/[y(y-1)]=∫dx
∫dy/(y-1)-∫dy/y =∫dx
ln(y-1)-lny=x+C
(y-1)/y=Ce^x
1-1/y=Ce^x
y=1/(1-Ce^x)

dy/[y(y-1)]=dx, dy[1/(y-1)-1/y]=dx,两边积分:ln|y-1|-ln|y|=x+lnc,
(y-1)/y=ce^x;