Quirky simplification (TI-92)


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Quirky simplification (TI-92)



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My TI-92 refused to cooperate in simplifying an expression today in my
Differential Equations class, and I was wondering if anyone out there has
had a similar experience, and/or knows why it did this.

Without going into all the details, I wanted to confirm that

    y(x) = (x/2 + 3/4) e^(x)

was a solution to

    y'' - 5y' + 6y = x * e^(x)

So I typed in
    (x/2 + 3/4)*e^(x) -> y(x)
    d(d(y(x),x),x) - 5 d(y(x),x) + 6y(x)

which resulted in the output

    -5(2x+5)e^x   3(2x+3)e^x    / x      \
    ----------- + ---------- + (  - + 3/4 ) e^x + e^x
          4            2        \ 2      /

I was surprised that it didn't come out simpler than this, but I typed in
    Expand(ans(1))
expecting to see it result in "x e^x" ... but it simply returned exactly the
same (unsimplified) expression!

A student with a TI-92+ was able to get the correct simplification (and
confirm that this y(x) really was a solution to the DE), but I finally had
to move on.  After class I experimented some more and discovered that
    Factor(ans(1))
and
    tExpand(ans(1))
both work (that is, they result in the simplified answer).

Can anyone reproduce (or explain) this?

--
Darryl K. Nester                E-mail: mailto:nesterd@bluffton.edu
Assoc. Prof. of Mathematics        WWW: http://www.bluffton.edu/~nesterd
Bluffton College                 Phone: 419-358-3483
Bluffton, OH  45817-1704           Fax: 419-358-3232

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