Re: [理工] [工數]-一階ode
※ 引述《ecko1023 (NEIGHBORHOOD)》之銘言：
: 1.
: 1
: y'+ ---y = y^2
: 2
: 這題我會解 可是算書來跟解答不一樣..
: 有大大幫忙一下嗎@@
: 答案是
: 1 1
: y= --- -----------
: 2 1-ce^1/2x
-2
同乘2y
-2 -1
2y y' + y = 2
-1 -2
設u = y u'= -y y'
-2u' + u = 2
2u'= u-2
2du = (u-2) dx
du 1
----- = --- dx
u-2 2
1
ln| u-2 | = ---x + c'
2
0.5x
u-2 = ce
0.5x
u = ce + 2
1
y = -----------
0.5x
ce + 2
: 2.
: dy
: cosx(e^2y-y) -----= e^ysin2x
: dx
: 答案是
: e^y+e^-y(y+1)=-2cosx+4
: 我想看步驟
: 我也是解出來 答案不一樣
: 都驗算過好幾次...
: 感恩感恩!!
2y y
cosx (e - y) y'=2e sinx cosx
y -y
(e - ye )dy = 2sinx dx
y -y -y
e + ye + e = -2cosx + c
y -y
e + (y+1)e = -2cosx + c
題目應該有給IC吧
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