[理工] [工數]-ode
周易課本P1-14習題1
y
Find orthogonal trajectories of x = y + 1 + ce
把方程式做微分
y
dx = dy + ce dy
y
dx = dy (1 + ce )
dy 1
---- = ----------
dx 1 + ce^y
dy l
假設另一曲線的斜率為 ----l 積分常數為a
dx lv
1 dy l
---------- ----l = -1 正交曲線斜率相乘為 -1
1 + ce^y dx lv
x - y - 1
c = ----------- 代入
e^y
1 dy
--------- ---- = -1
x - y dx
dy + (x - y) dx = 0
再來就積不下去了= =
請問我有哪邊算錯了嗎?
x
答案是 y = x + 1 + ae
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