Need Help with integral....

[dankman]

y'=2y + 5x⁴*e^2x

what i've done so far:

dy/dx = 2y +5x⁴*e^2x ==> S (-2y )dy = S 5x⁴e^2x dx ==>

-y² = ????

I can't seem to remember how to do these type of integrals. I think it should be something along the lines of 2x⁵*e^2x, but i'm not sure thats right

dan

 

[Lizzie]

I don't mean to be rude, but your post is a bit confusing. In order to keep things running smoothly, would you mind fixing it so that it is easier to understand? You can do this in any number of ways. For example, instead of using x^3 to say x³, simply write x < sup>3</ sup> without the spaces. Or, you could use LaTex. To find out exactly how to use LaTex, scroll your mouse over the "Forum Help" button at the top of your screen. You will see a drop down menu on which will be written a section on LaTex. If you take a look at the guide, you can figure it out and organize your problem. Thanks!

 

[Guest]

Hi Dank,
Looking at your problem, I'd think it was a linear first order DE :?:
So I'd have thought an integrating factor would do the trick once you've rearranged it, unless I'm not reading it right :lol:
You look to be seperating the variables I think, so maybe I'm not reading it right lol
Let me know if you are aware of integrating factors and such.
Cheers
Josh

 

[Unco]

G'day, Dankman.

Remember that if we were to seperate variables, we would divide, not subtract. But seperating variables is not going to work here.

As 03jwood has said, the integrating factor method is the way to go.

Write as
\(\displaystyle \L y' - 2y = 5x^4e^{2x}\)

\(\displaystyle \L \mu = e^{\int -2 \, dx} \, \, = e^{-2x}\)

etc.

 

[Lizzie]

\(\displaystyle \L y' - 2y = 5x^4e^{2x}\)

\(\displaystyle \L \mu = e^{\int -2 \, dx} \, \, = e^{-2x}\)

etc.

That was using LaTex. See how nice it looks? I hope that these posts have helped with your problem.

 

[Guest]

Sweet, are there any topics on here that describe how to use LaTex? I've been away for too long :lol:

 

[stapel]

Sweet, are there any topics on here that describe how to use LaTex?

Scroll up to the very top of the page, and use the "Forum Help" pull-down menu. The last three links should give you what you're looking for.

Eliz.

 

[pka]

If you are a Windows user, TeXaide is a free program.

 

[Lizzie]

It may look complicated at first, but after using it a few times, you'll start to get the hang of it, I promise! I am still learning mysefl.