求微分方程dy/dx=（4x+3Y）/(x+y)的通解
问题描述：
求微分方程dy/dx=（4x+3Y）/(x+y)的通解
答
把右边上下除x,再令y/x=u.则左边为u'x+u,接下来直接分离即可.
答
dy/dx=(4x+3y)/(x+y)dy/dx=3+x/(x+y)y/x=u dy=udx+xduu+xdu/dx=3+1/(1+u)xdu/dx=3-u+1/(1+u)(1+u)du/(4+2u-u^2)=dx/x(-1+u)du/(4+2u-u^2)-2du/(4+2u-u^2)=dx/x(-1/2)dln(4+2u-u^2)-2du/[5-(u-1)^2]=dlnxdu/[√5-(u-1...