       Re: Differential Eq.

• To: mathgroup at smc.vnet.net
• Subject: [mg106518] Re: [mg106478] Differential Eq.
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Fri, 15 Jan 2010 03:18:42 -0500 (EST)
• References: <201001141047.FAA19753@smc.vnet.net>

```Jamil Ariai wrote:
> Hi All,
>
> Can anybody kindly tell me how I can solve the following differential equation, with (x, x') = (0, 0):
>
> x''[t] -x[t] + g[t] = 0,
>
> where
>
> g[t] = b*v, for x'[t] > v,
> g[t] = b*(x'[t]-u), for Abs[x'[t]-u] < v, and
> g[t] = -b*v.
>
> Take b = 5, v = 0.2, and u = 0.1. Draw x[t] vs t, and x'[t] vs x[t].
>
> Thanks.
>
> J. Ariai

Could set it up as below.

soln = First[
With[{b = 5, v = 0.2, u = 0.1},
With[{gt =
Piecewise[{{b*v, x'[t] > v}, {b*(x'[t] - u),
Abs[x'[t] - u] < v}}, -b*v]},
NDSolve[{x''[t] - x[t] + gt == 0, x == 0, x' == 1.15},
x[t], {t, 0, 3}]]]]

If your initial derivative is one or less, the default handling seems to
run into trouble at one of the switches. I do not know why. Possibly
some Method or other settings can improve on that.

Daniel Lichtblau
Wolfram Research

```

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