Re: [考古] 成大99

[Eliphalet (真係廢到冇朋友)]

※ 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 .

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