Can anyone solve the Abel differential equation

x y \frac{dy}{dx} = x + y

It looks so easy (Shake)

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- Dec 24th 2008, 10:17 AMJesterhelp with a differential equation
Can anyone solve the Abel differential equation

x y \frac{dy}{dx} = x + y

It looks so easy (Shake) - Dec 24th 2008, 09:16 PMRapha
Hi!

Edit: Aaaargh, mr fantastic is right,

Edit: the following is the wrong:

$\displaystyle x*y \frac{dy}{dx} = x+y$

$\displaystyle x*y - y \frac{dy}{dx} = x$

$\displaystyle y (x-1) \frac{dy}{dx} = x$

$\displaystyle y \frac{dy}{dx} = \frac{x}{x-1}$

$\displaystyle \int y \frac{dy} = \int \frac{x}{x-1} dx$

$\displaystyle 0.5y^2 = ln(x - 1) + x + c$

....

Can you solve it now?

Edit: I made a big mistake... Sorry

Merry christmas,

Rapha - Dec 25th 2008, 04:31 AMmr fantastic
- Dec 25th 2008, 05:46 AMJester
- Dec 25th 2008, 02:22 PMmr fantastic
In the meantime, you might have a read of http://www.cecm.sfu.ca/CAG/papers/edgardoEJAM04.pdf

- Dec 25th 2008, 02:44 PMJester
- Dec 26th 2008, 05:30 PMHallsofIvy
Generally speaking, equations that have attracted enough interest to be given their own names are

**very**difficult!