[理工] [工數]-ODE
2 2 2 2
(x + 2xy - y )dx + (y + 2xy - x )dy = 0
已知積分因子為
1
I = -------
(x+y)^2
如果使用正合解法
答案是 (x^2+y^2)
----------- = C
(x+y)
但是如果用齊次的解法
答案相同
但是會多一個奇異解 y = -x
沒有辦法包含在通解中
如果把通解取倒數
變成
(x+y) 1
--------- = --- = K
(x^2+y^2) C
這下子奇異解就變成了 y = 正負ix
無論怎麼表示
都會有一組奇異解
那為何用正合解不會有奇異解呢?
希望好心人說明一下
謝謝 <(_ _)>
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