differential equation

drdolittle

somebody slove this differential equations

1/y' = (1/y)+(1/x)

thanx in advance

Zurtex

Perhaps looking at it like this:

[tex]\frac{1}{\frac{dy}{dx}} = \frac{1}{y} + \frac{1}{x}[/tex]

[tex]\frac{dx}{dy} = \frac{1}{y} + \frac{1}{x}[/tex]

[tex]x\frac{dx}{dy} = \frac{x}{y} + 1[/tex]

lol, I'll stop there because I suddenly realise this is beyond me (but it looks in a 'nicer' form, perhaps it will help you)

drdolittle

Your solution is just a peanut compared to where i have gone....there is still more to go...anyhow thanx for trying,do try nmore and figure out the solution.

regards
drdolittle

Zurtex

Well can you post what you have done please so others can help.

Zurtex

I ran this through Mathematica: DSolve[1/(y'[x]) == 1/x + 1/y[x], y[x], x]

And it gave me nothing sorry.

Edit: Although I'm not used to using Mathematica and have yet to get it to solve the simplest thing I think I have inputed it right.

drdolittle

try seperation of variables...after that iam struggling to cotinue....

daster

Even though I just started learning differential equations, I thought I'd give this a try:

[tex]\frac{dx}{dy}=\frac{1}{y}+\frac{1}{x}[/tex]

[tex]\frac{dy}{dx}=\frac{xy}{x+y}[/tex]

[tex]x\frac{dy}{dx}+y\frac{dy}{dx}=xy[/tex]

[tex]y+x\frac{dy}{dx}+y\frac{dy}{dx}=y+xy[/tex]

[tex]\frac{d(xy)}{dx}+\frac{1}{2}\frac{d(y^2)}{dx}=y(1+x)[/tex]

[tex]\frac{1}{y}\,d(xy)+\frac{1}{2y}\,d(y^2)=(1+x)\,dx[/tex]

I don't know what to do now, and I don't know if any of this is right, but I hope it'd be of some use.

Zurtex

Err I still think this is beyond me but I think you made a mistake on the LHS going from the 4th to the 5th line as:

[tex]\frac{d(xy)}{dx} = x\frac{dy}{dx} + y[/tex]

daster

I added a y to the LHS in the 4th step.

Integral

What I see when I look at that equation is a family of hyperbolas very much like the simple lens equation. There is a change of variables and a rotation that will reduce this equation to something which may be separable. Unfortunately I do not have the time to do all of the algebra for you.

Explore doing a change of variables, perhaps to polar coordinates, see what you get.

iSamer

How do you guys write the nice format of dy/dx and the fractions? Which program do you use, and you post them as photos?

I'll help in solving it, but after knowing how to post a math solution

Nylex

They use LaTeX. See this thread for more info .