Re: [微分] 兩題
※ 引述《xx52002 (長門有希好萌(′▽‵))》之銘言：
: (2)Let f and g be differential functions such that
: f'(x) = -g(x), g'(x) = f(x) for all x
: Suppose that f(a)=1, g(a)=0, prove that f^2(x)+g^2(x)=1
: 拜託各位了 @@
let h=f^2+g^2
h'=2ff'+2gg'=-2fg+2fg=0
so h is a constant, that is, h=c for all x
and h(a)=1, so c=1
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