Question

齐次方程(2√xy -y)dx+xdy=0的通解

Answer 1

2√(y/x)-y/x+dy/dx=0

令y/x=t^2

则y=t^2x,dy/dx=2xtdt/dx+t^2

2t-t^2+2xtdt/dx+t^2=0

2xdt/dx=-1

2dt=-dx/x

两边积分：2t=-lnx+C

(√y/x=)t=-ln√x+C

y=x(-ln√x+C)^2