→ owlran:我們應該考同個系，加油 XD 114.45.212.234 06/30 16:41
推 moonorblue:謝謝o大啦XD 加油 XD 220.141.41.39 06/30 22:06
※ 引述《moonorblue (mike)》之銘言：
: 有一題是
: Solve the differential equation
: y''-4y=6x-4x^3
: 該如何解呢?
y'' - 4y = 6x - 4x^3
=> y(D^2 - 4 ) = 6x - 4x^3
=> (D+2) (D-2) y = 6x - 4x^3
1
=> (D-2)y = _______ (6x - 4x^3)
D + 2
-2x 2x -2x
=> (D-2)y = e ∫e ( 6x - 4x^3 ) dx + C1 e
=> (D-2)y = -2x^3 + 3x^2 + C1e^(-2x)
1
=> y = _______ -2x^3 + 3x^2 + C1e^(-2x)
D - 2
2x -2x
=> y = e ∫e (-2x^3 + 3x^2 + C1e^(-2x) ) dx + C2e^(2x)
= x^3 - C1 e^(-2x)/4 + C2 e^(2x)
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 114.45.212.234