作业帮x*y的倒数-y=y^3的微分方程过程
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/24 04:40:50
x*y的倒数-y=y^3的微分方程过程
xy'-y=y^3
xdy/dx=y+y^3
dy/(y+y^3)=dx/x
dy/[y(1+y^2]=dx/x
d(y^2)/[y^2(1+y^2)]=2dx/x
d(y^2)*[1/y^2-1/(1+y^2)]=2dx/x
积分得：lny^2-ln(1+y^2)=2ln|x|+C1
y^2/(1+y^2)=Cx^2
再问： d(y^2)/[y^2(1+y^2)]=2dx/x这步我看不懂，能不再解释呀
再答： dy/[y(1+y^2]=dx/x, dy* y/[y^2(1+y^2)]=dx/x dy* 2y/[y^2(1+y^2)]=2dx/x d(y^2)/[y^2(1+y^2)]=2dx/x d(y^2)*[1/y^2-1/(1+y^2)]=2dx/x
xdy/dx=y+y^3
dy/(y+y^3)=dx/x
dy/[y(1+y^2]=dx/x
d(y^2)/[y^2(1+y^2)]=2dx/x
d(y^2)*[1/y^2-1/(1+y^2)]=2dx/x
积分得：lny^2-ln(1+y^2)=2ln|x|+C1
y^2/(1+y^2)=Cx^2
再问： d(y^2)/[y^2(1+y^2)]=2dx/x这步我看不懂，能不再解释呀
再答： dy/[y(1+y^2]=dx/x, dy* y/[y^2(1+y^2)]=dx/x dy* 2y/[y^2(1+y^2)]=2dx/x d(y^2)/[y^2(1+y^2)]=2dx/x d(y^2)*[1/y^2-1/(1+y^2)]=2dx/x