Question

(a) What can you say about a solution of the equation y' = −(1/6)y2 just by looking at the differential equation? The function y must be increasing (or equal to 0) on any interval on which it is defined. The function y must be strictly increasing on any interval on which it is defined. The function y must be decreasing (or equal to 0) on any interval on which it is defined.

Answer 1

$y^2\ge0$ for any $y$, and so $y'$ for all $y$, meaning $y$ is decreasing.