Merge pull request #1029 from benwalt/bug-4751

proposed fix for bugID 4751

Author: gajennings

OpenProblemLibrary/METU-NCC/Diff_Eq/linear-nonhomog.pg

@@ -115,12 +115,13 @@ $multiansB = MultiAnswer($y1, $y2, $Wronskian)->with(
           if (Formula("$S[0]*$dS[1]") == Formula("$S[1]*$dS[0]")) {
             Value::Error("Fundamental solutions not independent!");
           }
-          my @L = ( Formula("$ddS[0] - ($a+$b)*$dS[0] + ($a*$b)*$S[0]")->reduce, 
-                    Formula("$ddS[1] - ($a+$b)*$dS[1] + ($a*$b)*$S[1]")->reduce );
-          if ($L[0] == Formula("0")) { $flag[0] = 1; $msg = "\(y_1\) is fine$BR"; }
+
+          if (Formula("$ddS[0] - ($a+$b)*$dS[0]") == Formula("-($a*$b)*$S[0]")) 
+	        { $flag[0] = 1; $msg = "\(y_1\) is fine$BR"; }
           else  { $msg = "\(y_1\) is not a fundamental solution$BR"; }
 
-          if ($L[1] == Formula("0")) { $flag[1] = 1; $msg = $msg . "\(y_2\) is fine$BR"; }
+          if (Formula("$ddS[1] - ($a+$b)*$dS[1]") == Formula("-($a*$b)*$S[1]")) 
+	        { $flag[1] = 1; $msg = $msg . "\(y_2\) is fine$BR"; }
           else  { $msg = $msg . "\(y_2\) is not a fundamental solution$BR"; }
         }
 
@@ -220,13 +221,13 @@ $multiansD = MultiAnswer($gen_soln)->with(
        if (Formula("$S_h[0]*$dS_h[1]") == Formula("$S_h[1]*$dS_h[0]")) {
           Value::Error("Not the most general answer...");
        } 
-       if (Formula("$ddS_h[0] - ($a+$b)*$dS_h[0] + ($a*$b)*$S_h[0]") == Formula("0")) {
+       if (Formula("$ddS_h[0] - ($a+$b)*$dS_h[0]") == Formula("-($a*$b)*$S_h[0]")) {
           $msg = "\(y_1\) is okay$BR";
           $flag[0] = 1;
        } else {
           $msg = "\(y_1\) is wrong$BR";
        }
-       if (Formula("$ddS_h[1] - ($a+$b)*$dS_h[1] + ($a*$b)*$S_h[1]") == Formula("0")) {
+       if (Formula("$ddS_h[1] - ($a+$b)*$dS_h[1]") == Formula("-($a*$b)*$S_h[1]")) {
           $msg = $msg . "\(y_2\) is okay$BR";
           $flag[1] = 1;
        } else {