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This breaks my brain :(

Find f(x) when f'(x)=5f(x)

 Oct 3, 2019

Best Answer 

 #1
avatar+6045 
+3

\(\text{Your first differential equation!}\\ \text{I don't know how much you've been taught. The usual way to solve this is}\\ f'(x) = 5f(x)\\ \dfrac{f'(x)}{f(x)}=5\\ \text{Integrate both sides}\\ \ln(f(x)) = 5x+c\\ f(x) = e^{5x+c} = Ce^{5x}\)

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 Oct 3, 2019
 #1
avatar+6045 
+3
Best Answer

\(\text{Your first differential equation!}\\ \text{I don't know how much you've been taught. The usual way to solve this is}\\ f'(x) = 5f(x)\\ \dfrac{f'(x)}{f(x)}=5\\ \text{Integrate both sides}\\ \ln(f(x)) = 5x+c\\ f(x) = e^{5x+c} = Ce^{5x}\)

Rom Oct 3, 2019

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