Re: [微分]一題微分
※ 引述《n0204159 (黃黑人)》之銘言：
: f'(x)=5f(x)
: f(0)=3
: 問f(x)=?
: 感覺像高中的程度
: 我卻卡住了= =
令 y = f(x)
則 f'(x) = 5f(x) => y' = 5y
dy 1
---- = 5y => --- dy = 5 dx => ln|y| = 5x + c_1
dx y
|y| = e^(5x + c_1) = (e^(c_1))(e^(5x)) y = ±(e^(c_1))(e^(5x)) = k(e^(5x))
f(x) = k(e^(5x))
f(0) = 3 => k = 3 => f(x) = (3)(e^(5x))
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