Find all differentiable function for which $f'(x)=177f(x)$

$$\frac{f'(x)}{f(x)}=177$$ Integrating both sides with respect to $x$ gives $$\ln{(f(x))}=177x+C_1$$ $$f(x)=e^{177x+C_1}=C_2e^{177x}$$ Where $C_2=e^{C_1}$

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Real Analysis

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