推 winer8:第二題我猜是趨近的意思吧 12/16 17:17
→ winer8:後來第2提他的意思是y(0)=y'(0)=0 用來找c用的 12/16 23:11
※ 引述《winer8 (快來明星3 缺1 )》之銘言：
: 2
: y" 2(y')
: 1. ----- - ------- =0 ans:y=tan(c2+c1x)
: y 1+y^2
dp
令y' = p y' = p ──
dy
dp 2y
p [ ── - ──── ] = 0
p 1+y^2
p = 0 y = c 為trivial
2
ln│p│ = ln│1+y│ +c1
dy 2
p = ── = c1(1+y )
dx
dy
─── = c1dx
1+y^2
-1
tan y = c1x +c2
y = tan (c1x +c2)
: 2.y"-sinycosy=0
: 2
: (1)find (y') (2)as y--->0 ,y'--->0, find y
dp
令y = p y'= p──
dy
dp sin2y
p ─── - ──── = 0 積分
dy 2
cos2y
p^2 + ──── = c1
2
cos2y
(y')^2 = c1 - ────
2
(2)我看不懂耶= =
: ans: (1)c1-0.5cos2y (2)cscy-coty=c2e^(+-x)
: 2
: 3.yy"=2(y') -2y' y(0)=1 y'(0)=2
dp
令y= p y'= p──
dy
dp 2
yp── = 2p -2p
dy
dp
p[ y── - 2p + 2 ] =0
dy
p= 0 y = c 為trivial
1 dp dy
── ────── - ─── = 0
2 p - 1 y
1
── ln │p-1│ = ln│y│ + c1
2
p = 1 + c1y^2
dy
── = 1 + c1y^2
dx
代入ic c1 = 1
dy
───── = dx
1+ y^2
-1
tan y = x +c2
y = tan (x+c2)
y(0) = 1
π
c2 = ──
4
: pi
: ans: y=tan(x+---)
: 4
: 感謝各位了
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