Re: [理工] [工數]-高階O.D.E. by 逆算子
※ 引述《ncuatm (VC #15)》之銘言：
: 1. y" + y = -2sinx + 4xcosx
: 答案: y = c1cosx + c2sinx + 2xcosx + x^2sinx
: 這題yp我算出來是xcosx + x^2sinx 看了好多遍都找不出錯誤原因...
: 2. y"- 3y' - 4y = x^-3 * exp(4x) * (5x-2)
: 答案: y = c1exp(-x) + c2exp(4x) - x^-1 * exp(4x)
: 3. y" + y = secx * tanx
: 答案: y = c1cosx + c2sinx - sinx * ln|cosx| + x * cosx
: 麻煩解惑 感謝
2. 1
Yp = ------------ x^-3 * exp(4x) * (5x-2)
(D+1)(D-4)
1 5 -2
= exp(4x) ----------- ( ------ + ------ )
D(D+5) x^2 x^3
1 -5 1
= exp(4x) ------- ( ----- + ------ )
D+5 x x^2
-5 1
= exp(4x) * exp(-5x)∫exp(5x) ( ----- + ----- ) dx
x x^2
5 -1
= exp(-x) * -1 *∫exp(5x) (----- + ------- ) dx
x x^2
exp(5x)
= -1 exp(-x) * ----------
x
-exp(4x)
= ----------
x
我只能說..這是個好題目!!
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