设y=y(x)由x-∫1x+ye-t2dt=0确定,则=______.

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问题 设y=y(x)由x-∫1x+ye-t2dt=0确定,则=______.

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答案e-1

解析 当x=0时,y=1,x-∫1x+ye-t2dt=0两边对x求导,得1-e-(x+y)2=0.
将x=0,y=1代入得=e-1.
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