# Binary relation question

1. Sep 21, 2010

### Susanne217

1. The problem statement, all variables and given/known data

The binary relation $$\mathbb{R} \times (0, \infty)$$ which is identitical to

(as I understand it) $$\mathbb{R} \times \mathbb{R}_{+}$$

this is supposedly the set on which the solution of the differential equation

y' = f(t,y) is defined upon. Where y' = y/t + y^2 (no initial condition given).

I find the solution to be

y(t) = (2t)/(t^2 + c)

Then I am suppose to find all maximale solution on the interval above.

the solution is defined as follows on -infinity to infinity for an initial condition

y(t_0) = x_0 where t_0 > 0.

Because as I see it in Maple the solution phase portrait doesn't pass through zero if x_0 > 0.

Then I draw the phase portrait with the above condition the it look asymptotic?

But if I make x_0 then it I get what looks to be the real line.