设微分方程xy'+2y=2(ex一1). 补充定义使y0(x)在x=0处连续,求y'0(x),并请证明无论x≠0还是x=0,y'0(x)均连续,并请写出y'0(x)的表达式.

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问题 设微分方程xy'+2y=2(ex一1).
补充定义使y0(x)在x=0处连续,求y'0(x),并请证明无论x≠0还是x=0,y'0(x)均连续,并请写出y'0(x)的表达式.

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答案令[*] 而当x≠0时,[*] 所以[*] y'0(x)在x=0处连续.又显然,y'0(x)在x≠0处也连续,故无论x≠0还是x=0, [*] 均连续.

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