desolve y'=(x+y)^2

[salvomic]

(05-02-2015 05:30 AM)parisse Wrote:  Xcas can solve this equation. It is a Ricatti equation, you can solve it by giving a particular solution, otherwise the system rewrites it as a 2nd order equation.

thank you, Parisse.
The Xcas now is more updated than the CAS on Prime...
So, we hope that in the next FW upgrade of Prime it will be ok...

the type of equation is generally y' = f(ax+by+c) and the general solution can be got substituting u (in our case u=x+y -> u'=1+y' and so on)
The classic Riccati ODE is y'+g(x)y+h(x)y^2=k(x)

I had issue with a Riccati equation like \[ y' + \frac{2x+1}{x}y - \frac{1}{x}y^{2} = x+2 \]
Prime gives [], but the solution is \[ x + \frac{1}{1+cx} \]