Question

(x-2y)dy=2ydy,齐次方程的通解?

Answer 1

(x-2y)dx=2ydy

(x-2y)/2y=dy/dx

x/(2y)-1=y'

令y=px

y'=p'x+p

上式化为

1/(2p)-1=p'x+p

p'x=1/(2p)-p-1

dp/[1/(2p)-p-1]=dx/x

-2pdp/(2p^2+2p-1)=dx/x

好象不对啊