At Microsoft's Bing feature Chat I gave
two questions:
(1) My first question asked for a solution to
y'(t) = k y(t) (b - y(t))
Right away Chat noticed that this was
calculus and would involve exponential
growth. Then it gave me links to
references with examples of exponential
growth and differential equations.
But the response was nothing like a
solution, e.g., in TeX:
y(t) = { y(0) b e^{bkt} \over y(0) \big (
e^{bkt} - 1 \big ) + b }
So, Chat can respond with content about
differential equations but can't actually
solve an exercise in first calculus.
(2) I gave Chat the question:
Given triangle ABC, construct D on side AB
and E on side BC so that the lengths AD =
DE = EC.
Chat had no answer, not even a hint or
clue, how to do that.
But it did present some materials on
triangles, all either irrelevant or not
better than trivially relevant.
My Response: For some queries Chat may be
a little better than Bing or Google.
and the response: Given triangle ABC, we can construct D on side AB and E on side BC so that the lengths AD = DE = EC as follows:
Draw a line segment AC and construct its midpoint F. Draw a line segment BF and construct its midpoint G. Draw a line segment FG and extend it to intersect AC at point D. Draw a line segment BE and extend it to intersect AC at point E. Now, we have AD = DE = EC.
I hope this helps! Let me know if you have any other questions or if there’s anything else I can help you with.