Question

ydy-ydx+xdy=0

Answer 1

ydy/dx-y+xdy/dx=0

(y+x)dy/dx=y

dy/dx=y/(y+x)=1/(1+x/y).1

设t=x/y

x=yt

dx=tdy+ydt

代入1

(1+t)dy=tdy+ydt

dy=ydt

1/ydy=dt

同时积分

lny+c=t

lny-x/y+c=0