Re: [理工] [工數]-ODE
※ 引述《yooter231 (yooter)》之銘言：
: (1+xy)ydx+(1-xy)xdy=0 y(1)=1
: 拜託各位大大
(y+xy^2)dx +(x-x^2y)dy = 0
ydx+xdy - xy(xdy-ydx) = 0
dxy - xy(xdy-ydx) = 0
同除 (xy)^2 , u=xy
u^-2du - (xdy-ydx)/xy = 0
-u^-1 -ln(y/x) = c
- 1/xy - ln(y/x) = c
-1/1 - ln1 = c , c = -1
1/xy + ln(y/x) = 1
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