# Differential Equation help

1. Jan 24, 2005

### stunner5000pt

Doing a problem on the Uniqueness Theorem and i do not understand it

Can you help me by explaining why this example is unique or not, please?

Given $$\frac{dy}{dt} =F(t,y)$$
Also $$y_{1} = -1$$ for all t that are solutions
And $$y_{2} = 1+ t^2$$ for all t that are solutions
and y(0) = 0

Is the solution unique or not?

I think it is because y1(0) < y(0) <y2(0) . Is that the only criterion for uniqueness or is there something more?

2. Jan 25, 2005

### stunner5000pt

can someone simply explain the criteria for uniqueness for me?\

Maybe then i could get ahead on this problem!