※ 引述《stevegood (stevegood)》之銘言：
: 1.Consider the following general solution set of a DE
: y=c1X^2+c2exp(X)
: DE:y''+a1(x)y'+a0(x)y=f(x)
: Find a1(x),a0(x),f(x)
: 想知道高手們有沒有什麼好想法可以提供?
: 感謝瞜!
f(x) = 0
x -∫P(x)dx
y = c1 e = c1 e
1
P(x) = - 1
(D - 1)y = 0
2
把 y 代入 x
2
( 2x - x ) = z
-∫Q(x)dx
z = e
2
ln 2x - x = - ∫Q(x)dx
2 - 2x
───── = -Q(x)
2x - x^2
2x - 2
得解 (D + ────)(D - 1)y = 0
2x-x^2
2x - 2 2 - 2x
y'' + (1(-1) + ────)y' + (0 + ─────)y = 0
2x - x^2 2x - x^2
2
x - 2 2 - 2x
y'' + ───── y' + ───── y = 0
2x - x^2 2x - x^2
↑ ↑ ↑
a1 a0 f(x)
--
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 114.45.229.224