** Using WeBWorK **

We're getting a nice lot of posts here recently, so here's another one.

In our new differential equations homework set, I have the problem
solve \( $eqn \), where

  $whichQ = random(1,2,1);  # we write the equation two different ways
  $m = random(1,9,1);       #   to fool people into thinking they 
  $y1 = random(1,5,1);      #   have different problems.
  if ( $whichQ == 1 ) {
      $eqn = "x y' = -3 y + $m x^5; y(1) = $y1";
  } elsif ( $whichQ == 2 ) {
      $eqn = "{1\over x} y' + 3 {y\over x^2} = $m x^3; y(1) = $y1";
  }
  if ( $m == 8*$y1 ) {      # why is this necessary?  without the if
      $ans2 = "$m*x^5/(8)"; #   m==8y1, the correct answer y=x^5
  } else {                  #   (when y(0)=1 and m=8) wrong.
      $ans2 = "(-$m + $m*x^8 + 8*$y1)/(8*x^3)";
  }

As noted in the comment, without putting in the if to check whether the first and last terms in the answer cancel, in at least one case where they did the correct answer was marked wrong.

My first thought would be that the correct answer was being evaluated and returned something like 1.003E-08, so that the comparison in fun_cmp didn't work, but when I pass the answer to fun_cmp as a string I expect it to do the evaluation correctly. I (obviously) haven't done any experiments with this to figure out what's happening, but if someone can give me an answer off the top of their head I'd be interested in knowing what it is.

Thanks,
Gavin

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I had some problems with fun_cmp a year or two ago; I found it necessary to tweak the following values in the GLobal.pm file

$functZeroLevelDefault = 1E-12; $functZeroLevelTolDefault = 1E-12;

Cheers,

Tom

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