- #1

- 76

- 0

## Homework Statement

I'm starting college this autumn(physics) and I started learning some calculus on my own, basic stuff like first order differential equation and so on.Recently i stumbled on something that i don t understand.I was reading the course and re-solving the given examples for myself.So you have the equation

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

## Homework Equations

calculus

## The Attempt at a Solution

Given that the equation is already solved but i didn't understand one of the steps if the solutions i'll show you where i get stuck.

So you substitute y=tx and here comes the boom, by doing this substitution they say the result is

[tex] \frac{t+1}{t

^{2}+1}dt =-\frac{dx}{x} [/tex] and from here on it s quite simple, you just integrate both sides and get the result.But i didn't understand the steps from substituting y=xt to getting to that result.I ll show you how i tried to solve it but got to a different result.

So if y=tx --> dy/dx=tdx and it s clear that if you substitute dy/dx in that equation you don t get their answer.

My main problem is that, in high school we didn't use this notation, we used f'(x) instead of dy/dx and so on, so i'm having a bit of trouble getting used with this notation, but these are the one used in physics so now i have to squash my brains a little and try to get used to them.

If someone can explain that step to me and maybe give me a few tips on how to make the transition between these two notation easier it would be great!

Thank you

Last edited: