设P(x)在[0,+∞)连续且为负值,y=y(x)在[0,+∞)连续,在(0,+∞)满足y’+P(x)y>0且y(0)≥0,求证:y(x)在[0,+∞)单调增加.

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问题 设P(x)在[0,+∞)连续且为负值,y=y(x)在[0,+∞)连续,在(0,+∞)满足y’+P(x)y>0且y(0)≥0,求证:y(x)在[0,+∞)单调增加.

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答案由y’+P(c)y>0(x>0)[*]>0 (x>0),又[*]y(x)在[0,+∞)连续, [*]y(x)在[0,+∞)单调[*] [*]y(x)>0(x≥0)[*]y’(x)>一P(x)y(x)>0 (X>0)[*]y(x)在[O,+∞)单调增加.

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