       Re: Manipulate a Plot of Evaluate DSolve

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• Subject: [mg127516] Re: Manipulate a Plot of Evaluate DSolve
• From: Juan Barandiaran <barandiaran.juan at gmail.com>
• Date: Wed, 1 Aug 2012 04:54:09 -0400 (EDT)
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• References: <20120729070521.C7CB3684D@smc.vnet.net> <CAEtRDSfuzxN12HoeTLPuZGmegBOpubxd3J_g0ESgnT8=KQStBw@mail.gmail.com>

```Thanks Bob,

Yes, I could use NDSolve instead of DSolve, in my case I'm only getting
numerical outputs, so it should do the job.

But in the example that you send me, why is nothing plotted?

Thanks again and best regards,

Juan

2012/7/30 Bob Hanlon <hanlonr357 at gmail.com>

> If DSolve cannot solve the equations then use NDSolve.
>
> func[coef_?NumericQ, c_?NumericQ, x_?NumericQ] :=
>  y[t] /. NDSolve[{y'[t] == Cos[coef*t], y == c},
>      y[t], {t, -10, 10}][] /. t -> x
>
> Manipulate[Plot[
>   Evaluate[func[coef, c, x] /. c -> Range],
>   {x, -10, 10},
>   PlotRange -> {-5, 10}],
>  {{coef, 1}, 0.1, 5, 0.01,
>   Appearance -> "Labeled"}]
>
>
> Bob Hanlon
>
>
> On Sun, Jul 29, 2012 at 6:12 PM, Juan Barandiaran
> <barandiaran.juan at gmail.com> wrote:
> > Of course your solution works, but I still don't understand why mine
> doesn't
> > and I cannot use your proposed approach because the way you write the
> > problem it is easy for Mathematica to solve the DSolve.
> > And this is just a simple example, in my real problem the DSolve cannot
> be
> > solved analytically.
> > This is why I tried to express the function as:
> >
> > {{y -> Function[{x}, DSolve[y'[x] == Cos[coef *x], y, x]]}}
> >
> > , which is something like the output I get from my DSolve.
> >
> > Thanks for your help.
> >
> > Juan
> >
> >
> > 2012/7/29 Bob Hanlon <hanlonr357 at gmail.com>
> >>
> >> Clear[func];
> >>
> >> func[coef_, c_, x_] =
> >>  y[x] /. DSolve[{y'[x] == Cos[coef*x], y == c}, y[x], x][] //
> >>   Simplify
> >>
> >> c + Sin[coef*x]/coef
> >>
> >>
> >> Manipulate[Plot[Evaluate[
> >>    func[coef, c, x] /.
> >>     c -> Range],
> >>   {x, -10, 10},
> >>   PlotRange -> {-5, 10}],
> >>  {{coef, 1}, 0.1, 5, 0.01,
> >>   Appearance -> "Labeled"}]
> >>
> >>
> >> Bob Hanlon
> >>
> >>
> >> On Sun, Jul 29, 2012 at 3:05 AM,  <barandiaran.juan at gmail.com> wrote:
> >> > Hi,
> >> >
> >> > I'm trying to Manipulate a Plot of a quite difficult function which
> >> > involves solving a differential equation, but cannot be solved
> analytically.
> >> >
> >> > To try to simplify the example and simulate it, let's assume that we
> >> > have the following function:
> >> >
> >> > func[coef_] = {{y -> Function[{x}, DSolve[y'[x] == Cos[coef *x], y,
> >> > x]]}}
> >> >
> >> > Manipulate[Plot[{{Evaluate[y[x] /. func[coef] /. C -> {Range[-5,
> >> > 0]}]}}, {x, -10, 10}], {{coef , 1}, 0.1, 5}]
> >> >
> >> > I get an error: DSolve::dsvar: "-9.99959 cannot be used as a variable"
> >> >
> >> > I think that this is because Manipulate assigns a value to x (=
> >> > -9.99959) BEFORE solving the DSolve, even though to avoid it I'm
> using the
> >> > Evaluate function, which should process the function before assigning
> a
> >> > value to x.
> >> >
> >> > But the thing is that the "coef" to be Manipulated is at the same
> >> > "level" as the x in the Manipulate block, so probably if I need the
> coef to
> >> > solve the DSolve, I also have the x that gives me an error.
> >> >
> >> > Is there any workaround? I guess I'm not understanding properly how
> >> > Mathematica processes these simple expressions.
> >> >
> >> > Thanks, Juan
> >> >
> >
> >
>

```

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