Steps of solving differential equatations

[dudeperfect]

I missed few practices on University, now I have a bunch of theory about differential equatations, I read it all, and trying to solve some of them, but I would like to ask for a steps I should take to solve differential equatations.

So for example I have a equatation like this:

\(\displaystyle x^2\, +\, y^2\, -\,2xyy'\, =\, 0\)

What I first do is trying to make a equatation like this: y' = everything else.
Then I change y' to dy/dx and trying to move x near dx and y near dy.

Is it the correct way of solving this? Maybe you have some tips.

 

[Ishuda]

I missed few practices on University, now I have a bunch of theory about differential equatations, I read it all, and trying to solve some of them, but I would like to ask for a steps I should take to solve differential equatations.

So for example I have a equatation like this:

\(\displaystyle x^2\, +\, y^2\, -\,2xyy'\, =\, 0\)

What I first do is trying to make a equatation like this: y' = everything else.
Then I change y' to dy/dx and trying to move x near dx and y near dy.

Is it the correct way of solving this? Maybe you have some tips.

If you do that you get

\(\displaystyle y'\, =\,\dfrac{x^2\, +\, y^2}{2\, x\, y}\)

which doesn't appear to help.

However, when I see a yy' in an equation [or a y' = something/y], I am always tempted, just from experience, to make a substitution of \(\displaystyle y\, =\, \sqrt{x}\, u\). You might try that and see what -2xyy' is.