Question

What can you say about a solution of the equation y' = (1/2)y2 just by looking at the differential equation?

Answer 1

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.

Learn more about differential equations here:

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