Question in understanding differitial equations

1. May 11, 2008

transgalactic

i have started to learn this stuff
and it looks like a normal derivative stuff but its different
i dont know how to find a general solution
what is the algorithm to act on??

here is a simple example:
http://img381.imageshack.us/my.php?image=26202865up1.jpg
i was told to find a general solution

i dont know how to isolate Y i am not sure
what i need to do here
its so much different

????

2. May 11, 2008

Hootenanny

Staff Emeritus
It looks very much like an http://mathworld.wolfram.com/ExactDifferential.html" [Broken] to me.

Last edited by a moderator: May 3, 2017
3. May 11, 2008

Defennder

No, it's not an exact differential equation... yet. You have to multiply the entire expression throughout by something to make it exact, then you can solve it by that method.

4. May 11, 2008

transgalactic

i too see it as an exact differential
it looks like the one in the article

why its not an exact differential??

Last edited: May 11, 2008
5. May 12, 2008

Defennder

They differ by a factor of -1.

6. May 12, 2008

transgalactic

how did you get -1??

there are two variables here
there could be also derivatives in one of them

how did you get the factor?

7. May 12, 2008

Defennder

I did this: $$\frac{\partial}{\partial y} \ \frac{y}{x} = \frac{1}{x}$$
$$\frac{\partial}{\partial x}\ \left(y^2-lnx\right) = -\frac{1}{x}$$.

That's why I said they differ by factor of -1.

8. May 12, 2008

transgalactic

what does the expression d/dx represent

when i did derivatives there were only dx not "d"

???

9. May 12, 2008

Defennder

Uh, which expression? This one: $$\frac{\partial}{\partial x}$$? That's partial differentiation. It means to say differentiate a multi-variable function with respect to x alone.

10. May 13, 2008

transgalactic

11. May 14, 2008

Defennder

Actually I don't know what you're writing:

Specifically, what does $$d(ln|y|) \ \mbox{and} \ d(ln|x|)$$ mean?

12. May 14, 2008

transgalactic

i recognized 1/x and 1/y as a derivatives of ln|x| and ln|y|

thats the only integrals i saw there

i read that i am supposed to see patterns of integrals
and solve them

but its not working here
???

Last edited: May 14, 2008
13. May 14, 2008

Defennder

I really have no idea what you are saying. What patterns of integrals are you talking about?

14. May 14, 2008

transgalactic

i/x i recognized as the derivative of ln|x|

how to solve this correctly

15. May 14, 2008

Defennder

I don't know how that is related to this question. I'll just refer you to these notes, then maybe you can apply the technique here.

A differential equation of the form $$N(x,y) \ dy + \ M(x,y) \ dx =0$$ is considered exact if $$\frac{\partial M}{\partial y} \ = \ \frac{\partial N}{\partial x}$$.

Eg. $$x \ dy -y \ dx = 0$$ is not exact. But it can be made to be exact by multiplying throughout by the 1/x^2:

$$\frac{1}{x} \ dy - \frac{y}{x^2} \ dx = 0$$

See here for more details on the topic:
http://tutorial.math.lamar.edu/Classes/DE/Exact.aspx

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