7.3 Separable Equations

Mathematica script by Chris Parrish,
   cparrish@sewanee.edu

Sources and references for some of these problems include
    James Stewart, "Calculus: Concepts and Contexts," Second Edition, Brooks/Cole, 2001
    Deborah Hughes-Hallett, Andrew M. Gleason, et. al., "Calculus," Second Edition, John Wiley & Sons, 1998
    Robert Fraga, ed., "Calculus Problems for a New Century," The Mathematical Association of America, 1993

Slope Field for dy/dx = x/y

Hughes-Hallett, Gleason, et al, First Edition, Exercise 9.4.28, page 500

In[488]:=

<<Graphics`Colors`
<<Graphics`PlotField`

In[490]:=

Clear[f,x,y,a,b,c,d];

f[x_,y_] := x/y;

a = 0.1; b = 0.5;    (* a <= x <= b *)
c = 0.1; d = 0.5;    (* c <= y <= d *)

pts = {{0.2,0.2}};

field = PlotVectorField[{1,f[x,y]},
                        {x,a,b},{y,c,d},
                        PlotLabel -> "dy/dx = x/y",
                        Axes -> True,
                        AxesLabel -> {"x","y"},
                        PlotPoints -> 15,
                        Prolog -> ManganeseBlue,
                        Epilog -> {Red,PointSize[0.02],
                                   Map[Point,pts]}];

[Graphics:HTMLFiles/7.3_separableEquations_1.gif]

Slope Field for dy/dx = -y/x

Hughes-Hallett, Gleason, et al, First Edition, Exercise 9.4.29, page 500

In[496]:=

Clear[f,x,y,a,b,c,d];

f[x_,y_] := -y/x;

a = 0.1; b = 0.5;    (* a <= x <= b *)
c = 0.1; d = 0.5;    (* c <= y <= d *)

pts = {{0.2,0.2}};

field = PlotVectorField[{1,f[x,y]},
                        {x,a,b},{y,c,d},
                        PlotLabel -> "dy/dx = -y/x",
                        Axes -> True,
                        AxesLabel -> {"x","y"},
                        PlotPoints -> 15,
                        Prolog -> ManganeseBlue,
                        Epilog -> {Red,PointSize[0.02],
                                   Map[Point,pts]}];

[Graphics:HTMLFiles/7.3_separableEquations_2.gif]


Created by Mathematica  (April 25, 2004)