# Question about a Linear 1st Order DE

[SOLVED] Question about a Linear 1st Order DE

1. The problem statement, all variables and given/known data
Find the general solution to $$\frac{dy}{dx}=5y$$

Now I know that this is separable. But it is in the exercise set that immediately follows "finding a general solution" in which they use variation of parameters. At least I think that is what it is called...when for y'+P(x)y=f(x) you find the integrating factor $\mu(x)=e^{\int P(x)dx}[/tex] Now if I solve by separation: $$\frac{1}{5}\frac{dy}{y}=dx$$ $$1/5\ln y=x+C$$ <----is there a preference of where the C goes (with x or y)? By Var of Parameters: since P=-5, [itex]\mu(x)=e^{-5x}$

$$e^{-5x}*y=C$$

Now is $$1/5\ln y=x+C$$ equivalent to $$e^{-5x}*y=C$$?

I mean they must be, but I just can't see it.

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I see it!! Exponentiate!

"Question about a Linear 1st Order DE"

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