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Re: Manipulate a Plot of Evaluate DSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg127494] Re: Manipulate a Plot of Evaluate DSolve
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Mon, 30 Jul 2012 03:44:43 -0400 (EDT)
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• References: <20120729070521.C7CB3684D@smc.vnet.net>

Clear[func];

func[coef_, c_, x_] =
 y[x] /. DSolve[{y'[x] == Cos[coef*x], y[0] == c}, y[x], x][[1]] //
  Simplify

c + Sin[coef*x]/coef


Manipulate[Plot[Evaluate[
   func[coef, c, x] /.
    c -> Range[5]],
  {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[1] -> {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
>

• References:
  • Manipulate a Plot of Evaluate DSolve
    • From: barandiaran.juan@gmail.com