(************** Content-type: application/mathematica **************
                     CreatedBy='Mathematica 5.0'

                    Mathematica-Compatible Notebook

This notebook can be used with any Mathematica-compatible
application, such as Mathematica, MathReader or Publicon. The data
for the notebook starts with the line containing stars above.

To get the notebook into a Mathematica-compatible application, do
one of the following:

* Save the data starting with the line of stars above into a file
  with a name ending in .nb, then open the file inside the
  application;

* Copy the data starting with the line of stars above to the
  clipboard, then use the Paste menu command inside the application.

Data for notebooks contains only printable 7-bit ASCII and can be
sent directly in email or through ftp in text mode.  Newlines can be
CR, LF or CRLF (Unix, Macintosh or MS-DOS style).

NOTE: If you modify the data for this notebook not in a Mathematica-
compatible application, you must delete the line below containing
the word CacheID, otherwise Mathematica-compatible applications may
try to use invalid cache data.

For more information on notebooks and Mathematica-compatible 
applications, contact Wolfram Research:
  web: http://www.wolfram.com
  email: info@wolfram.com
  phone: +1-217-398-0700 (U.S.)

Notebook reader applications are available free of charge from 
Wolfram Research.
*******************************************************************)

(*CacheID: 232*)


(*NotebookFileLineBreakTest
NotebookFileLineBreakTest*)
(*NotebookOptionsPosition[     77599,       2120]*)
(*NotebookOutlinePosition[     78244,       2142]*)
(*  CellTagsIndexPosition[     78200,       2138]*)
(*WindowFrame->Normal*)



Notebook[{

Cell[CellGroupData[{
Cell[BoxData[
    \(DSolve[\(y'\)[x] \[Equal] \((\((x - y[x] + 1)\)/\((x + y[x] - 3)\))\), 
      y[x], x]\)], "Input"],

Cell[BoxData[
    \({{y[x] \[Rule] 
          3 - x - \@\(\((\(-3\) + x)\)\^2 + 2\ \((x + x\^2\/2)\) + C[1]\)}, \
{y[x] \[Rule] 
          3 - x + \@\(\((\(-3\) + x)\)\^2 + 2\ \((x + x\^2\/2)\) + \
C[1]\)}}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(a[x_, c_] = 
      3 - x - \@\(\((\(-3\) + x)\)\^2 + 2\ \((x + x\^2\/2)\) + C\)\)], "Input"],

Cell[BoxData[
    \(3 - 
      x - \@\(C + \((\(-3\) + x)\)\^2 + 2\ \((x + x\^2\/2)\)\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(b[x_, c_] = 
      3 - x + \@\(\((\(-3\) + x)\)\^2 + 2\ \((x + x\^2\/2)\) + C\)\)], "Input"],

Cell[BoxData[
    \(3 - 
      x + \@\(C + \((\(-3\) + x)\)\^2 + 2\ \((x + x\^2\/2)\)\)\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
    \(Plot[
      Evaluate[Table[a[x, C], {C, \(-3\), 3, 1}]], {x, \(-2\), 
        5}]\), "\[IndentingNewLine]", 
    \(Plot[
      Evaluate[Table[b[x, C], {C, \(-3\), 3, 1}]], {x, \(-2\), 
        5}]\), "\[IndentingNewLine]", 
    \(\)}], "Input"],

Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: .61803 
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% Graphics
%%IncludeResource: font Courier
%%IncludeFont: Courier
/Courier findfont 10  scalefont  setfont
% Scaling calculations
0.295918 0.136054 0.565289 0.0649205 [
[.02381 .55279 -6 -9 ]
[.02381 .55279 6 0 ]
[.15986 .55279 -6 -9 ]
[.15986 .55279 6 0 ]
[.43197 .55279 -3 -9 ]
[.43197 .55279 3 0 ]
[.56803 .55279 -3 -9 ]
[.56803 .55279 3 0 ]
[.70408 .55279 -3 -9 ]
[.70408 .55279 3 0 ]
[.84014 .55279 -3 -9 ]
[.84014 .55279 3 0 ]
[.97619 .55279 -3 -9 ]
[.97619 .55279 3 0 ]
[.28342 .04592 -12 -4.5 ]
[.28342 .04592 0 4.5 ]
[.28342 .17577 -12 -4.5 ]
[.28342 .17577 0 4.5 ]
[.28342 .30561 -12 -4.5 ]
[.28342 .30561 0 4.5 ]
[.28342 .43545 -12 -4.5 ]
[.28342 .43545 0 4.5 ]
[ 0 0 0 0 ]
[ 1 .61803 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 g
.25 Mabswid
[ ] 0 setdash
.02381 .56529 m
.02381 .57154 L
s
[(-2)] .02381 .55279 0 1 Mshowa
.15986 .56529 m
.15986 .57154 L
s
[(-1)] .15986 .55279 0 1 Mshowa
.43197 .56529 m
.43197 .57154 L
s
[(1)] .43197 .55279 0 1 Mshowa
.56803 .56529 m
.56803 .57154 L
s
[(2)] .56803 .55279 0 1 Mshowa
.70408 .56529 m
.70408 .57154 L
s
[(3)] .70408 .55279 0 1 Mshowa
.84014 .56529 m
.84014 .57154 L
s
[(4)] .84014 .55279 0 1 Mshowa
.97619 .56529 m
.97619 .57154 L
s
[(5)] .97619 .55279 0 1 Mshowa
.125 Mabswid
.05102 .56529 m
.05102 .56904 L
s
.07823 .56529 m
.07823 .56904 L
s
.10544 .56529 m
.10544 .56904 L
s
.13265 .56529 m
.13265 .56904 L
s
.18707 .56529 m
.18707 .56904 L
s
.21429 .56529 m
.21429 .56904 L
s
.2415 .56529 m
.2415 .56904 L
s
.26871 .56529 m
.26871 .56904 L
s
.32313 .56529 m
.32313 .56904 L
s
.35034 .56529 m
.35034 .56904 L
s
.37755 .56529 m
.37755 .56904 L
s
.40476 .56529 m
.40476 .56904 L
s
.45918 .56529 m
.45918 .56904 L
s
.48639 .56529 m
.48639 .56904 L
s
.51361 .56529 m
.51361 .56904 L
s
.54082 .56529 m
.54082 .56904 L
s
.59524 .56529 m
.59524 .56904 L
s
.62245 .56529 m
.62245 .56904 L
s
.64966 .56529 m
.64966 .56904 L
s
.67687 .56529 m
.67687 .56904 L
s
.73129 .56529 m
.73129 .56904 L
s
.7585 .56529 m
.7585 .56904 L
s
.78571 .56529 m
.78571 .56904 L
s
.81293 .56529 m
.81293 .56904 L
s
.86735 .56529 m
.86735 .56904 L
s
.89456 .56529 m
.89456 .56904 L
s
.92177 .56529 m
.92177 .56904 L
s
.94898 .56529 m
.94898 .56904 L
s
.25 Mabswid
0 .56529 m
1 .56529 L
s
.29592 .04592 m
.30217 .04592 L
s
[(-8)] .28342 .04592 1 0 Mshowa
.29592 .17577 m
.30217 .17577 L
s
[(-6)] .28342 .17577 1 0 Mshowa
.29592 .30561 m
.30217 .30561 L
s
[(-4)] .28342 .30561 1 0 Mshowa
.29592 .43545 m
.30217 .43545 L
s
[(-2)] .28342 .43545 1 0 Mshowa
.125 Mabswid
.29592 .07839 m
.29967 .07839 L
s
.29592 .11085 m
.29967 .11085 L
s
.29592 .14331 m
.29967 .14331 L
s
.29592 .20823 m
.29967 .20823 L
s
.29592 .24069 m
.29967 .24069 L
s
.29592 .27315 m
.29967 .27315 L
s
.29592 .33807 m
.29967 .33807 L
s
.29592 .37053 m
.29967 .37053 L
s
.29592 .40299 m
.29967 .40299 L
s
.29592 .46791 m
.29967 .46791 L
s
.29592 .50037 m
.29967 .50037 L
s
.29592 .53283 m
.29967 .53283 L
s
.29592 .01346 m
.29967 .01346 L
s
.29592 .59775 m
.29967 .59775 L
s
.25 Mabswid
.29592 0 m
.29592 .61803 L
s
0 0 m
1 0 L
1 .61803 L
0 .61803 L
closepath
clip
newpath
.5 Mabswid
.02381 .58539 m
.06244 .59032 L
.10458 .59509 L
.14415 .59884 L
.16408 .60039 L
.18221 .60155 L
.20178 .60251 L
.20694 .60271 L
.21254 .6029 L
.2178 .60304 L
.22272 .60315 L
.22726 .60323 L
.22982 .60326 L
.23216 .60329 L
.23339 .6033 L
.2347 .6033 L
.23546 .60331 L
.23615 .60331 L
.23685 .60331 L
.23749 .60332 L
.23874 .60332 L
.2394 .60332 L
.2401 .60332 L
.24127 .60332 L
.24255 .60331 L
.24323 .60331 L
.24396 .60331 L
.2453 .6033 L
.2478 .60328 L
.25073 .60324 L
.25343 .6032 L
.25835 .60309 L
.26358 .60294 L
.27295 .60256 L
.28305 .602 L
.29259 .60131 L
.30133 .60053 L
.32026 .5983 L
.34096 .59492 L
.36057 .59071 L
.38152 .58497 L
.42302 .56942 L
.463 .54881 L
.50147 .52392 L
.54238 .49275 L
.58179 .45909 L
.61967 .42418 L
.66001 .38497 L
.69884 .34578 L
.74011 .30295 L
Mistroke