# Differential equations, qualitative solution

MaxManus
dy/dt = -ty^2 y(0) = 1
What can you say about the solution over the interval 0<=t <=2?

The text says that the solution is decreasing and never zero because y(t) = 0 for all t is an equilibrium solution.

I can see why the solution can never cross the x-axis, but why can't the solution become zero?

Homework Helper
What did you get for the solution y(t)?

MaxManus
I got y = $$\frac{1}{t^2 + 1}$$, but I got the impression that looking at the derivative was enough to make the conclusion

MaxManus
Anyone?

Homework Helper
Anyone?

if it crosses the t-axis, then shouldn't y=0 ? and what does that mean?

MaxManus
if it crosses the t-axis, then shouldn't y=0 ? and what does that mean?

Yes, but why can't it become zero and stay there?

Homework Helper
Yes, but why can't it become zero and stay there?

How exactly would it become zero? That would mean that at some value of 't' the corresponding value of 'y' would be zero.

$$0 = \frac{1}{t^2+1}$$

You would end up with a false equality, which can only mean that y(t) is never zero for all values of t.