Re: [理工] [工數]-高階ode
※ 引述《winer8 (快來明星3 缺1 )》之銘言：
: 標題: [理工] [工數]-高階ode
: 時間: Sun Aug 16 00:42:39 2009
:
: y''-3y'-4y=1/(x^3) * exp(4x) * (5x-2)
:
: yp=1/(D^2-3D-4) * (5x-2)exp(4x)/x^3
:
: =1/(D-4)(D+1) * d(exp(4x)/x^2)/exp(x)
:
: =1/(D-4) * exp(-x) S d(exp(4x)-x^2)
:
: =1/(D-4) * exp(3x)/x^2
:
: =exp(4x) * S exp(-x)/x^2
: 到這步我就不會積了 答暗是 -exp(4x)/x
2 4x 3
yp = 1 / ( D - 3D - 4 ) (5x-2)e / x
4x 3
yp = 1 / (D-4)(D+1) (5x-2)e / x
-x 5x -4x 4x 3
yp = e S e S e (5x-2)e / x dx
-x 5x 2
yp = e S e [ (-5/x) + (1/x ) ] dx
-x 5x 5x 2 5x 2
yp = e [ -(e /x ) - S e (1/x ) dx + S e (1/x ) dx ]
4x
yp = -e / x
希望沒解錯...
:
:
: 另一題 (3x-4)^2y''+3(3x-4)y'+36y=0
:
: 我算答案是y=C1/(3x-4)*cos[11^1/2*ln(3x-4)]+C2/(3x-4)*sin[11^1/2*ln(3x-4)]
:
: 解答是 y=c1*cos(2ln(3x-4))+c2*sin(2ln(3x-4))
: 不知道有沒有錯
: 感謝各位了
:
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