# College Math Teaching

## September 23, 2014

### Ok, what do you see here? (why we don’t blindly trust software)

I had Dfield8 from MATLAB propose solutions to $y' = t(y-2)^{\frac{4}{5}}$ meeting the following initial conditions:

$y(0) = 0, y(0) = 3, y(0) = 2$.

Now, of course, one of these solutions is non-unique. But, of all of the solutions drawn: do you trust ANY of them? Why or why not?

Note: you really don’t have to do much calculus to see what is wrong with at least one of these. But, if you must know, the general solution is given by $y(t) = (\frac{t^2}{10} +C)^5 + 2$ (and, of course, the equilibrium solution $y = 2$). But that really doesn’t provide more information that the differential equation does.

By the way, here are some “correct” plots of the solutions, (up to uniqueness)