Re: [理工] [工數]-高階ODE
※ 引述《mdpming (ｎＥｗ)》之銘言：
: 1.
: 2 2
: yy'' - (y') - y y' = 0
dp 2 2
py ── - p - py = 0
dy
2 2
py dp - (p + py ) dy = 0
py dp - p^2dy - py^2dy = 0
p(ydp - pdy) - py^2dy = 0
p = 0 y = C trivial
2 p 2
y d(──) - y dy = 0
y
y = 0 trivial
p
d(──) - dy = 0
y
p/y - y = c1
2
p = c1y + y
dy
────── = dx
c1y + y^2
A B
──── - ──── dy = dx
y c1 + y
c1 A + Ay - By = 0
A = B
A = 1/c1
1 1 1
── ( ─── - ──── ) dy = dx
c1 y c1 + y
ln y - ln c1 + y = c1 x + c2
y
──── = c1x + c2
c1 + y e
c1 c1x + c2
1 - ──── = e
c1 + y
-c1
──────── = c1 + y
c1x
C2 e - 1
c1x
- c1C2 e
y = ────────────
c1x
C2 e - 1
同除就知道囉^.^
: 答案
: c1
: y = ----------------
: -c1*x
: c2*e - 1
: 怎麼移都移不出來 還是我算錯了@@
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