Can anyone solve the Abel differential equation
x y \frac{dy}{dx} = x + y
It looks so easy
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
In the meantime, you might have a read of http://www.cecm.sfu.ca/CAG/papers/edgardoEJAM04.pdf