(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Question about a Linear 1st Order DE

1. The problem statement, all variables and given/known data

Find the general solution to [tex]\frac{dy}{dx}=5y[/tex]

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 [itex]\mu(x)=e^{\int P(x)dx}[/tex]

Now if I solve by separation:

[tex]\frac{1}{5}\frac{dy}{y}=dx[/tex]

[tex]1/5\ln y=x+C[/tex] <----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}[/itex]

[tex]e^{-5x}*y=C[/tex]

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

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Question about a Linear 1st Order DE

**Physics Forums | Science Articles, Homework Help, Discussion**