- #1

amcavoy

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- Mathematica
- Thread starter amcavoy
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- #1

amcavoy

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- #2

lurflurf

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yes there isapmcavoy said:

- #3

amcavoy

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Well, how would I do it?

- #4

lurflurf

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Graphics`PlotField`

that may be helpfull

all you need for particular curves is to define a function using DSolve or NDSolve

f[x_,x0_,y0_]:=NDSolve[{y'[x]+y[x]==0,y[x0]==y0},y[x],{x,y0,10}][1,1,2]

for the slope field use the DE to get the slope

- #5

saltydog

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Hey Apmcavoy, can you follow this (note the double equal signs):

A plot of the results is attached. If so, can you post the same for your differential equation?

Edit: Alright, you don't need some of that stuf: arrow tip at the end of the curve, the axes->True, thickness, plotstyle, plotpoints. Just take them out to cut it down.

Code:

```
<<Graphics`PlotField`
<<Graphics`Arrow`
sol1=NDSolve[{y'[x]==y[x]-x,y[0]==0.5},y,{x,0,3}];
fsol[x_]:=Evaluate[y[x]/.Flatten[sol1]];
xpt=2.6
xed=2.7
ypt=fsol[2.6]
yed=fsol[2.7]
a1=Graphics[Arrow[{xpt,ypt},{xed,yed}]];
pv=PlotVectorField[{1,y-x},{x,-3,3},{y,-3,3},PlotRange->{{-4,4},{-4,4}},
PlotPoints->25,Axes->True]
pt1=Plot[fsol[x],{x,0,2.7},PlotStyle->{{Thickness[0.01]}}]
Show[{pv,pt1,a1}]
```

A plot of the results is attached. If so, can you post the same for your differential equation?

Edit: Alright, you don't need some of that stuf: arrow tip at the end of the curve, the axes->True, thickness, plotstyle, plotpoints. Just take them out to cut it down.

Last edited:

- #6

amcavoy

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- #7

saltydog

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apmcavoy said:

Quicker? How about this stripped-down version:

Code:

```
<<Graphics`PlotField`
sol1=NDSolve[{y'[x]==y[x]-x,y[0]==0.5},y,{x,0,3}];
pt1=Plot[Evaluate[y[x]/.sol1]
pv=PlotVectorField[{1,y-x},{x,-3,3},{y,-3,3}]
Show[{pt1,pv}]
```

- #8

amcavoy

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- #9

saltydog

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apmcavoy said:

Alright I'm sorry. That's what I get for posting it without trying it first. Some typos: (no x range in Plot). Also the <<Graphics line should be in it's own cell as it needs to be executed only once to load the package (PlotField is a library of functions).

Code:

```
<<Graphics`PlotField`
sol1=NDSolve[{y'[x]==y[x]-x,y[0]==0.5},y,{x,0,3}];
pt1=Plot[Evaluate[y[x]/.sol1,{x,0,3}]
pv=PlotVectorField[{1,y-x},{x,-3,3},{y,-3,3}]
Show[{pt1,pv}]
```

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