       Re: Question about how to graph the vector field for the differential

• To: mathgroup at smc.vnet.net
• Subject: [mg97896] Re: Question about how to graph the vector field for the differential
• From: Bluefly <jo1e984 at gmail.com>
• Date: Wed, 25 Mar 2009 05:42:26 -0500 (EST)
• References: <gq7j9f\$qeo\$1@smc.vnet.net> <gqacnl\$j8j\$1@smc.vnet.net>

```On 3\$B7n(B24\$BF|(B, \$B>e8a(B3\$B;~(B30\$BJ,(B, "Sjoerd C. de Vries" <sjoerd.c.devr... at gmail.com>
wrote:
> I have the feeling you're looking for the wrong type of plot. Your
> differential equation yields a family of funtions of x and these can
> be plotted simply by using Plot.
>
> First, solve the differntial equation:
>
> In:= DSolve[y'[x] == 2 x - y[x], y[x], x]
>
> Out= {{y[x] -> 2 (-1 + x) + E^-x C}}
>
> Then plot it for some values of the constant C:
>
> Plot[Table[2 (-1 + x) + E^-x c, {c, -10, 10, 5}] // Evaluate, {x, -1,
>   5}, PlotRange -> All]
>
> Cheers -- Sjoerd
>
> On Mar 23, 11:03 am, jo1e... at gmail.com wrote:
>
> > i need to graph the vector field and the family of solutions for the
> > DE: dy/dx=2x-y
> > and i tried the graph the vector field, but while i tried to use the
> > VectorFieldPlot it show up some kind of wierd graph...
> > and i cannot even get start on the "family of Solutions"
> > graph...searched online but still cannot figure out.
> > hope some pros can help me out on this...thx alot~!!
> > Bluefly

thx for the answers...
that really helped me on the part where i need the "family of
solutions"....

but i dont understand is that why isnt the vector field or direction
field work on this? =(
i remember i saw someone used it and graph bunch of arrows along with
the solution's direction...
what i mean is that on the graph there are many arrows (vectors) that
kinda filled up the graph....and the directions of the vectors are the
same as the solution graph.

btw, how to graph the orthogonal trajectories along the same function?
thank you all for the help
Bluefly

```

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