Re: Ti-92 Integration
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Re: Ti-92 Integration
Junaid Mansuri writes:
> How would I solve for y in the following equation on the Ti-92:
> dy/dx=x/y
>
> I need a symbolic answer for y
>
> Also is there a way to integrate an expression like x/y on the
> calculator?
>
> I know you can integrate x^2+3x+2, but that ony has one variable, how
> would I integrate something like x/y, to solve for y???
Look in your text under ÒSeparation of VariablesÓ or ÒSeparable EquationsÓ.
If you can, by algebraic manipulation, transform a given DE into the form
f(x)dx = g(y)dy, then you can (in principle) take antiderivatives to get an
equation F(x) = G(y) + C, which you can (again in principle) solve for y to
get an explicit solution to the original DE.
In the present case, all these steps can be performed immediately,
"by inspection" -- there should be absolutely no need to use a powerful
tool such as the TI-92 (it would be like swatting a mosquito with a shovel).
If students are using TI-92s or similar software, then you ought to be
looking at tougher (and more interesting) problems.
There are three distinct steps in the above outline of a solution that might,
for a given problem, pose a challenge to the non-assisted solver: the
original separation of variables, the finding of antiderivatives, and the
final solution for y. It would be an interesting challenge to design examples
where each of these steps, in turn, would be non-trivial enough to
(practically) require assistance from a symbolic calculator.
Calling for solution in the last two steps is conceptually straightforward:
you just ask the TI-92 for the indefinite integral with respect to a given
variable or for solving an equation for a given variable. It is the first
step that is the interesting one. There are some limits on the ability of the
TI-92's solving capabilities, and sometimes it is necessary to "help" the
calculator with insightful moves. How many people use the idea of putting an
equation as an object into the TI-92 and wrestle with it formally (e.g.
by squaring the equation, subtracting quantities from both sides,
removing a factor, etc.)? Of course this both makes a good classroom
demo (with an overhead display) and can serve as the basis of a
_script_ that could be distributed to students for individual work.
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
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