记y=f(x)
则dy/dx=y
dy/y=dx
积分：ln|y|=x+c1
则y=ce^x
代入y(0)=1,得c=1
故y=e^x
即f(x)=e^x
证明:若函数f(x)在(-∞,+∞)内满足不等式f'(x)=f(x),且f(0)=1,则f(x)=e∧x
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