# Question in understanding differitial equations

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

????

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

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Defennder
Homework Helper
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.

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

why its not an exact differential??

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Defennder
Homework Helper
They differ by a factor of -1.

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?

Defennder
Homework Helper
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.

what does the expression d/dx represent

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

???

Defennder
Homework Helper
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.

Defennder
Homework Helper
Actually I don't know what you're writing:

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

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
???

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

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

how to solve this correctly

Defennder
Homework Helper
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