Re: [考古] 師大考古題~~
※ 引述《MrTang (堂先生)》之銘言：
: Solve the intial problem:
: dy exp^x^2
: (x+1)-- -2(x^2+x)y= --------- ,x>1 y(0)=6
: dx x+1
: 請問一下這題要怎樣解....
: 能說一下解法..或者是打出來~~~謝謝~
dy e^(x^2)
(x+1)(----) - (2)(x^2 + x)(y) = ---------
dx x + 1
dy e^(x^2)
---- - (2)(x)(y) = ----------- ------(1)
dx (x + 1)^2
∫-2x dx -(x^2)
(1)的積分因子 = e = e
-(x^2)
(1)*(e )
dy 1
=> (e^(-(x^2)))(----) - (2x)(e^(-(x^2)))(y) = -----------
dx (x + 1)^2
d((e^(-(x^2)))(y)) 1
=> -------------------- = -----------
dx (x + 1)^2
-1
=> (e^(-(x^2)))(y) = ------- + c
x + 1
-1
=> y = (-------)(e^(-(x^2))) + (c)(e^(-(x^2)))
x + 1
y(0) = 6
=> 6 = (-1)(1) + (c)(1) => c - 1 = 6 => c = 6 + 1 = 7
-1
y = (-------)(e^(-(x^2))) + (7)(e^(-(x^2)))
x + 1
--
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07/05 20:56, , 1F
07/05 20:56, 1F
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