→ nicewine1 :I donot know if there is another solution 09/19 23:55
推 playmypig :先謝,因為老師像是要我們用代入法來做,但我不懂,你這 09/20 00:29
→ playmypig :樣做我也很明白啊,謝謝 09/20 00:29
推 SS327 :先找交點 在平移 09/20 02:19
→ RAINDD :"微分方程式"的解是....？ 09/20 11:02
※ 引述《playmypig (玩我豬)》之銘言：
: 請各位指教了, 我不知道如何入手, 圖片如下:
: http://holland.pk/fYM
(x-y+1)dy=(x+3y-1)dx
x(dy)-(ydy)+dy = xdx + 3ydx - dx
xy- 1/2(y^2) +y = 1/2(x^2) + 3xy - x
1/2(x^2+y^2) +2xy = x+y
x^2 + y^2 + 4xy = 2(x+y)
(x+y)^2 + 2xy = 2(x+y)
(x+y)^2 - 2(x+y) = -2xy
(x+y)(x+y-2) = -2xy
(1) If x=0 => y(y-2)=0 => y=0 or y=2
(2) If y=0 => x(x-2)=0 => x=0 or x=2
so the solution is (0,0) (0,2) or (2,0)
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