1. Dif EQ

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

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

2. 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 $y=t^2$ and $y=t^2+1$ in terms of your equation.

--Kevin C.