[理工] [工數]-微方的解答我看不懂(逆運算)
題目:
y"-3y'-4y= [(e^4x)*(5x-2)]/x^3
解答:
特性方程式為~
m^2-3m-4=0
m= -1 , 4
齊次解為~
Yh = A*e^-x + B*e^4x
特解~
1 e^4x (5x-2)
Yp = __________*{_____________} <-----A式
D^2 -3D -4 x^3
e^4x 5x-2
= __________*________ <-----B式
D^2 +5D x^3
e^4x -5 1
= __________*( _____ + _____ )
D +5 x x^2
-5 1
= (e^4x)*(e^-5x)∫(e^5x)*( _____ + _____ ) dx
x x^2
-e^4x
= _______
x
ODE通解為~
e^4x
Y(x)= Yh + Yp = A*e^-x + B*e^4x - ________
x
想請問~~~
A式是如何變成B式的?
尤其是D^2 -3D -4變成D^2 +5 更是令我苦思不得其解
求高手幫忙 Orz
感謝
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 124.9.201.230
→
08/04 20:43, , 1F
08/04 20:43, 1F
推
08/04 20:46, , 2F
08/04 20:46, 2F
→
08/04 20:47, , 3F
08/04 20:47, 3F
→
08/04 20:48, , 4F
08/04 20:48, 4F
※ 編輯: johnoldman 來自: 124.9.201.230 (08/04 21:17)
→
08/04 21:19, , 5F
08/04 21:19, 5F
推
08/04 21:19, , 6F
08/04 21:19, 6F
→
08/04 21:24, , 7F
08/04 21:24, 7F
推
08/04 21:26, , 8F
08/04 21:26, 8F