→ topee:y大只能用線性嗎?? 我那邊是哪裡積錯? 04/12 23:39
→ ytyty:不一定啊~只是線性感覺比較快又好做XD 04/12 23:42
→ iyenn:順手就好~_~ 04/12 23:43
推 gn00648013:正合也可以～ 04/12 23:58
推 stevenmanjj:令u=x+y+1....做變數變換...也蠻快的喔 04/13 00:12
※ 引述《topee (eason)》之銘言：
: dy 1
: ---= ------
: dx x+y+1
dx
─ = x+y+1
dy
dx
─ -x = y+1 ...(1)
dy
∫-1dy -y
I.F.= e = e
-y
(1)式乘以e 得
-y dx -y -y
e ─ -e x = (y+1)e
dy
d -y -y
─[e x] = (y+1)e
dy
-y -y
e x = ∫(y+1)e dy
-y -y -y -y -y -y
∫ye dy=∫-y[e ]' dy = -ye - ∫(-y)'e dy = -ye + ∫e dy
-y -y -y
所以 e x = -ye + 2 ∫e dy
-y -y
e x = (-y-2)e + c
y
x = -y-2 + ce
--
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