idku
  • idku
Am I solving this DE correctly?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
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idku
  • idku
I am just tryng some substitution problems. y' = ln(y+x)
idku
  • idku
(this particular prob, I made up) z = y + x z' = y' +1 y' = z' - 1 z' - 1 = ln(z) z' = ln(z) + 1 1/ (ln(z) + 1) • (dz/dx) = 1 then I integrate both sides with respect to x, and get: Integral, 1/ (ln(z) + 1) dz= x
Astrophysics
  • Astrophysics
I guess that should work, you got a separable right?

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Astrophysics
  • Astrophysics
Actually, I don't really know what the Ei here is, wolfram gave this http://www.wolframalpha.com/input/?i=y%27%3Dln%28y%2Bx%29 maybe @zepdrix @IrishBoy123 can help you with this one
idku
  • idku
After the v sub, it is separable, but then I have an obstacle when it comes to integrating. Well, this isn't something that I so far really know how to integrate.... Wolfram gives me: \(\color{black}{\dfrac{{\rm Ei}(\log(z)+1)}{e}}\)
idku
  • idku
It would be good if someone explains what this Ei really is.
Astrophysics
  • Astrophysics
Oh it says "Ei(x) is the exponential integral Ei" ok still no idea haha
idku
  • idku
Yes, that is my prob as well.
idku
  • idku
I guess I will just take a note of this for now, and will dig into it later.... because I don't think I have a proper base knowledge for this. It seems too complex. I am better start of some normal examples on the web.... didn't mean to disturb anyone.
IrishBoy123
  • IrishBoy123
https://en.wikipedia.org/wiki/Exponential_integral
IrishBoy123
  • IrishBoy123
@SithsAndGiggles
IrishBoy123
  • IrishBoy123
@freckles
idku
  • idku
Irishboy, it's ok.
idku
  • idku
Thank you though
Astrophysics
  • Astrophysics
@Zarkon
freckles
  • freckles
looks like: \[\int\limits_{}^{} \frac{e^x}{x} dx =Ei(x)+C \\ \int\limits \frac{1}{\ln(v)+1} dv \\ u=\ln(v)+1 \\ u-1=\ln(v) \\ e^{u-1}=v \\ e^{u-1} du=dv \\ \int\limits \frac{1}{u} e^{u-1} du =\frac{1}{e} \int\limits \frac{e^u}{u} du=\frac{1}{e} Ei(u)+C \\ =\frac{1}{e} Ei(\ln(v)+1)+C\]

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