(x-ycosy/x)dx+xcosy/xdy=0
1个回答

1-y/x*cos(y/x)+cos(y/x)*dy/dx=0

令y/x=u,则dy/dx=u+xdu/dx

所以1-ucosu+cosu*(u+xdu/dx)=0

cosu*xdu/dx=-1

cosudu=-dx/x

两边积分:sinu=-ln|x|+C

u=y/x=arcsin(-ln|x|+C)

y=xarcsin(-ln|x|+C)