Given the Dif EQ $\displaystyle \frac{dy}{dt}=-y^2+y+2yt^2+2t-t^2-t^4$

Show if $\displaystyle y(t)$ is a sol'n to the Dif EQ and if $\displaystyle 0<y(0)<1$, then $\displaystyle t^2<y(t)<t^2+1$ for all $\displaystyle t$.

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- Dec 12th 2007, 01:46 PM #1

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## Solution curves

Consider the fact that the solution curves of a first degree differential equation cannot cross (as at the point of a hypothetical crossing, they would have to have the same values of t and y but different y' values, and thus could not both be solutions to the same first order differential equation).

Now look at $\displaystyle y=t^2$ and $\displaystyle y=t^2+1$ in terms of your equation.

--Kevin C.