作者Eliphalet (真係廢到冇朋友)
站內trans_math
標題Re: [考古] 成大99
時間Tue Jul 3 17:59:27 2012
※ 引述《Highhuman (Ryan)》之銘言：
: For a differential equation x^2 y" -3xy' +4y = 0,
: (a)use z = lnx to transform such an equation into an equation with constant
: coefficients
: (b)find the general solution of (a) in terms of x.
: 這題爬文後，還是不懂...
: 感覺目的好像是利用 z=lnx 把y'和y"換掉而以...
: 可以麻煩詳細說明嗎?! @@"
就照做啊... 這種是 Cauchy-Euler type 的 ODE
Put Y(z) = y(e^z)
z= ln x => y'(x) = Y'(z) * 1/x
=> y"(x) = Y"(z) * (1/x)^2 - Y'(z) * 1/x^2
Sub. y' y" into the original equation
=> Y"(z) - Y'(z) - 3 * Y'(z) + 4 Y(z) = 0
解 Y .
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 203.101.240.116
1F：→ Highhuman:略懂!!111.249.226.104 07/03 18:58
2F：→ Highhuman:general solution 怎寫?!111.249.226.104 07/03 19:23
3F：→ Eliphalet:Y(z) = a e^(2z) + b z*e^(2z)203.101.240.116 07/03 19:41
4F：→ Eliphalet:a,b consts203.101.240.116 07/03 19:42
5F：推 Highhuman:thx111.249.226.104 07/03 19:45