[理工] [微方] 一階ODE

看板Grad-ProbAsk作者 (桶三洨!!!)時間14年前 (2011/05/28 23:54), 編輯推噓6(6推 0噓 6→)
留言12則, 6人參與, 最新討論串1/1
EX: y ( 1 -xy + x^2*y^2 ) dx + x ( x^2*y^2 - xy ) dy = 0 SOL: y = 1/x [1+-根號(ln(c/x)] 但我是算 y = 1/x [1+-根號(ln(c/x^2)] 有高手可以幫解惑嗎? -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 218.164.50.246
推
05/29 00:26, , 1F
妳對
05/29 00:26, 1F
→
05/29 00:27, , 2F
ydx-xydxy+x^2y^2dxy=0
05/29 00:27, 2F
→
05/29 00:28, , 3F
dx/x+(xy-1)dxy=0 積分
05/29 00:28, 3F
推
05/29 00:30, , 4F
整理後就跟你一樣
05/29 00:30, 4F
→
05/29 00:52, , 5F
可以請問你是用什麼方法嗎 我的方法有點煩
05/29 00:52, 5F
推
05/29 01:03, , 6F
grouping method
05/29 01:03, 6F
→
05/29 01:11, , 7F
我會了 感謝各位大大的回答
05/29 01:11, 7F
推
05/29 18:51, , 8F
如果不確定答案對不對就帶回去驗算一下
05/29 18:51, 8F
推
05/29 19:16, , 9F
x^2 y^2/2 - xy + ㏑ x = C = ㏑√(c/e)
05/29 19:16, 9F
→
05/29 19:16, , 10F
y(x) = 1/x [1 ± √(ln(c/x^2)]
05/29 19:16, 10F
推
05/31 22:01, , 11F
令u=xy y'=(u/x)' 代入求解
05/31 22:01, 11F
→
09/11 14:24, , 12F
令u=xy y'=( https://daxiv.com
09/11 14:24, 12F
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文章代碼(AID): #1DuHgeLi (Grad-ProbAsk)