Re: [微方] 請問這題該怎麼解呢

看板trans_math作者amymayyam (殘缺的愛)時間20年前 (2005/10/04 22:28)推噓15(15推 0噓 6→)

留言21則, 4人參與討論串3/3 (看更多)

※ 引述《finalgod (0_o安ㄚ)》之銘言： : ※ 引述《sjwei (哈)》之銘言： : : determine a region of xy-plane for which the : : given differential eq. would have a unique : : solution whose graph passes through a pont : : (x0,y0) in the region. : : (y - x) y' = y + x : : 謝謝大家 : (y - x) dy = (y + x) dx : 令 du = (x + y) dx + (x - y) dy : ------- ------- : M N : δM/δy = 1 ，δN/δx = 1，exact : u[x,y] = ∫(x + y)dx + φ[y] = (1/2)x^2 + xy + φ[y] = (1/2)C : δu[x,y]/δy = x + φ'[y] = x - y =0，φ'[y] = - y ，φ[y] = - (1/2)y^2 : u[x,y] = (1/2)x^2 + xy - (1/2)y^2 = (1/2)C ，令 f[x,y] = 2u[x,y] : f[x,y] = x^2 + 2xy - y^2 = C 用全微分一下就出來嚕 (y-x)dy=(y+x)dx (x-y)dy+(x+y)dx=0 xdy+ydx-ydy+xdx=0 左右兩邊取積分 2xy-y^2+x^2=C -- 220 除了本身以外的因數有:1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110 284 除了本身以外的因數有:1, 2, 4,71,142 而 220=1+2+4+71+142 284=1+2+4+5+10+11+20+22+44+55+110 它們彼此付出了自己的全部而化成了對方.... adapted from MagicFox.... -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 218.164.75.126

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finalgod

10/04 23:22, , 1^F

10/04 23:22, 1^F

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amymayyam

10/04 23:43, , 2^F

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amymayyam

10/04 23:43, , 3^F

10/04 23:43, 3^F