→ finalgod:畫出來的圖形是斜的雙曲線 09/27 01:28
→ finalgod:註：當C＝0時為一點，當C≠0才是雙曲線 09/27 01:39
→ finalgod:正確地說應是當C＝0時為y＝(1±√2)x兩線相交於一點 09/29 20:07
※ 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
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