Re: [理工] [工數]-級數解
看板Grad-ProbAsk作者ntust661 (Enstchuldigung~)時間15年前 (2010/04/19 18:52)推噓3(3推 0噓 4→)留言7則, 3人參與討論串27/32 (看更多)
※ 引述《laboy10 (開學了>"<)》之銘言：
: 2
: d 2
: ____ y(x) - x y(x) = 0
: 2
: dx
: y(x = ±∞) = 0
: 2
: y(x)≒exp[-x /2 ]
: 麻煩高手指點一下
n-2 n + 2
Σ (n)(n-1)an x - Σ an x = 0
n=2 n=0
n+2 n + 2
Σ (n+4)(n+3)an+4 x - Σ an x = 0
n=-2 n=0
2 a2 = 0
6 a3 = 0
an
an+4 = ──────────
(n+4)(n+3)
a0
a4 = ──
12
a1
a5 = ──
20
a2
a6 = ── = 0
30
a7 = 0
a4 a0
a8 = ─── = ───────
56 3 * 4 * 7 * 8
4 8 5
x x x
y = a0 (1 + ── + ──── + ... ) + a1 (x + ── + ...)
12 672 20
這是個在 x → ±∞ 都會發散的數列
並不會趨近於零@@
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