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# First order differential equation

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1. First order differential equation
I need to solve:

Ln(y^x). dy/dx = 3x^2 . y
Rearrange to get

X.lny (dy) = 3x^2 (dx)
Int (X.lny (dy)) = Int (3x^2 (dx))

To get

(lny)^2/2 = 3x^2/2 + C

According to my mark scheme I should get C/2
But I don't know why?
2. Re: First order differential equation
- try integrating by parts (where u = ln y, and dv/dy = 1)

Also, I don't see where your y from the first line has gone.
And if you're finding c, then you'll have been given x and y values which you haven't stated in your post.

Edit: And ignore the first two parts as they have been corrected below - next time try and keep the y in your working throughout, but equally (if not more so) it's my bad for not trying with it first ).
Last edited by starkrush; 19-04-2012 at 17:57.
3. Re: First order differential equation
(Original post by claret_n_blue)
....
To integrate ln(y)/y use substitution:

let u= lny

du/dy = 1/y

du= dy/y

-> I u du = u^2/2= (lny)^2/2.
4. Re: First order differential equation
http://www.wolframalpha.com/input/?i...dx+%3D+3x%5E2y

Wolfram says no constant/2.

Not quite sure where that constant/2 has come from, I certainly don't get that either.
5. Re: First order differential equation
(Original post by starkrush)
...
Wrong.

OP is correct, if I'm interpreting correctly.
Last edited by f1mad; 19-04-2012 at 17:46.
6. Re: First order differential equation
(Original post by f1mad)
Wrong.

OP is correct, if I'm interpreting correctly.
Ninja edited 1 minute before you replied

And edited to reflect this clearer
Last edited by starkrush; 19-04-2012 at 17:58.
7. Re: First order differential equation
(Original post by starkrush)
Ninja edited 1 minute before you replied

And edited to reflect this clearer
Last edited by f1mad; 13 Minutes Ago at 16:46

Last edited by starkrush; 1 Minute Ago at 16:57.

8. Re: First order differential equation
That was to strikethrough the text!

(Yes, this is very constructive maths help)

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Last updated: April 19, 2012
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