Re: [理工] [工數]-簡單ODE ~"~

看板Grad-ProbAsk作者ytyty (該換個版潛水了™ )時間16年前 (2010/04/12 23:31)推噓2(2推 0噓 3→)

留言5則, 5人參與討論串3/4 (看更多)

※ 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 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 218.162.224.68

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topee

04/12 23:39, , 1^F

04/12 23:39, 1^F

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ytyty

04/12 23:42, , 2^F

04/12 23:42, 2^F

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iyenn

04/12 23:43, , 3^F

04/12 23:43, 3^F