# differential equation

by drdolittle
Tags: differential, equation
 P: 27 somebody slove this differential equations 1/y' = (1/y)+(1/x) thanx in advance
 HW Helper Sci Advisor P: 1,123 Perhaps looking at it like this: $$\frac{1}{\frac{dy}{dx}} = \frac{1}{y} + \frac{1}{x}$$ $$\frac{dx}{dy} = \frac{1}{y} + \frac{1}{x}$$ $$x\frac{dx}{dy} = \frac{x}{y} + 1$$ 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)
 P: 27 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
HW Helper
P: 1,123

## differential equation

Well can you post what you have done please so others can help.
 HW Helper Sci Advisor P: 1,123 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.
 P: 27 try seperation of variables...after that iam struggling to cotinue....
 P: n/a Even though I just started learning differential equations, I thought I'd give this a try: $$\frac{dx}{dy}=\frac{1}{y}+\frac{1}{x}$$ $$\frac{dy}{dx}=\frac{xy}{x+y}$$ $$x\frac{dy}{dx}+y\frac{dy}{dx}=xy$$ $$y+x\frac{dy}{dx}+y\frac{dy}{dx}=y+xy$$ $$\frac{d(xy)}{dx}+\frac{1}{2}\frac{d(y^2)}{dx}=y(1+x)$$ $$\frac{1}{y}\,d(xy)+\frac{1}{2y}\,d(y^2)=(1+x)\,dx$$ 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.
 HW Helper Sci Advisor P: 1,123 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: $$\frac{d(xy)}{dx} = x\frac{dy}{dx} + y$$
 P: n/a I added a y to the LHS in the 4th step.
 Mentor P: 7,206 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.
 P: 4 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
P: 555
 Quote by 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