I never thought I'd be the one to ask for homework help here, but I really hate math, so here goes. I'm doing differentials. Pretty simple separable DEs, or linear first-order DEs. I can do the integration to solve no problem, but I can't seem to rearrange this equation into either of the following forms: dy * f(y) = dx * g(x) or dy/dx + P(x) * y = f(x) where dy/dx = y' = the derivative of y with respect to x So yeah, if anyone could give rearranging this a shot (really, you don't need to know calculus to do this, it's more algebra...) I'd appreciate it. I've given it a good 3-4 shots now, and I'm stumped. The problem I'm looking at is: dy/dx = (x^2 - y^2)/(x * y) Thanks for anyone who tries!
Why don't you try wolframalpha.com? Maybe all you need is to put dy/dx = (x^2 - y^2)/(x * y) in the input box.
I assume you're just trying to find a formula for y? Wolfram Alpha is a pretty powerful website, but I tried plugging this problem into it and it didn't give me a very nice looking solution. However, I did manage to reduce it to a simple integration problem, no differential equations required. Take the formula you already have, dy/dx = (x^2 - y^2)/(x * y), and carry out the division. This gives you dy/dx = x/y - y/x. Now just integrate both sides with respect to x (which allows you to treat the y as a constant, like you'd do with, say, a 2). That will leave you wish a y on the left, and a formula with x's and y's on the right. From there it's just algebra to isolate the y. I leave the rest to you; my tutoring sensibilities won't let me give it all away.
Maybe expand the brackets and differentiate y in respect to x So dy = x.y(x-x^2) . actually, couldnt you integrate in some way and then simplify it. =/ Maths sucks sometimes. Let us know hwo you worked it out, hopefully if you doo xD
I did try Wolfram-ing it before I posted this thread, but like you said, it gave me a nasty answer... and really, I don't learn anything by cheating (except the lesson that tells me I'll do terrible on the test for cheating on the assignments xD). Anyway, the prof gave out a hint recently that said to do a substitution, so I followed through with that and solved it (let v = y^2, dv = 2ydy) just fine. That was basically what Wolfram did, but at least I did it myself? Honestly, it's that "in-the-box" thinking that screws me over for math. I would've never thought to use substitution outside of direct integration. Durrrr. I tried integrating it like you said, but I didn't get the correct answer. It's possible I just integrated incorrectly or didn't do the algebra properly. When I get back home (with my scanner), if I post up my work would you mind telling me if/where I went wrong? Unless it's simply a case of you really can't solve the problem that way. Regardless, thanks everyone for the help.
sry for this bold answer, but it's already 02:38 am here. separation won't work here unless you use a substitution. dy/dx = (x^2 -y^2)/xy = (x^2 - y^2)*(x^-1 y^-1) expand brackets dy/dx = x^(2-1)*y^-1 - y^(2-1)*x^-1 = x/y - y/x now you'll have to substitute one of the terms x/y or y/x with a new variable v to separate the DE. I can try and give you a more explicite answer when I had some sleep