> logic

I see. Yes, you would want the min, but it would fail for (x/y + y/x). So I think you want to try solve for x in the power and if you can, use that as in

```
>>> solve(x**-1*y-t,x)
[y/t]
>>> (x/y+y/x).subs(x, _[0])
t + 1/t
>>> solve(x**2*y-t,x)
[-sqrt(t/y), sqrt(t/y)]
>>> (x**2*y + x**4*y**2).subs(x, _[0])
t**2 + t
>>> solve(x**2*y-t,x)
[-sqrt(t/y), sqrt(t/y)]
>>> (x**2*y + x**3*y).subs(x, _[0])
t - y*(t/y)**(3/2)
```

It doesn't matter which root you pick (if there are multiple) if all powers are even, but what if you had x**6*y**3? Does this matter for your ode?

> work without it

Yes, I guess the t-test would fail.