函数f(x)满足f'(x)=f(x)+1,且f(0)=0,则f(x)=______ f'(x)是f(x)的导数,

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函数f(x)满足f''(x)=f(x)+1,且f(0)=0,则f(x)=______f''(x)是f(x)的导数,函数f(x)满足f''(x)=f(x)+1,且f(0)=0,则f(x)=______f''(x

函数f(x)满足f'(x)=f(x)+1,且f(0)=0,则f(x)=______ f'(x)是f(x)的导数,
函数f(x)满足f'(x)=f(x)+1,且f(0)=0,则f(x)=______
f'(x)是f(x)的导数,

函数f(x)满足f'(x)=f(x)+1,且f(0)=0,则f(x)=______ f'(x)是f(x)的导数,
只有e^x的导数是它本身,所以可以设
f（x）=k*e^x+b
则f'(x)=k*e^x
又因为f'(x)=f(x)+1,
k*e^x=k*e^x+b+1
所以b+1=0 b=-1
因为f(0)=0,将x=0 b=-1代入f（x）=k*e^x+b
求出k=1
所以f（x）=e^x-1

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