The function y must be equal to 0 on any interval on which it is defined. The function y must be increasing (or equal to 0) on any interval on which it is defined.
Analysis of solution by seeing differential equation:
Given differential equation is: y' = (1/2)y2
How do deduce the results just by seeing them?
The equation tells us that:
rate = positive of ( y^2 )
rate = positive of (positive or zero) = positive or zero
Thus, the rate is positive or zero no matter what value we put in the place of y from its valid domain, since.
When the rate is positive or zero, that means the function will never grow upwards. Thus, either increasing or staying at the same level.
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