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MathGroup Archive 2004

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Re: UnitStep Function in ODE

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47762] Re: UnitStep Function in ODE
  • From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
  • Date: Mon, 26 Apr 2004 02:40:52 -0400 (EDT)
  • References: <c6d7q5$jdp$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Mathematica 5.0.1 gives

{{y[t] -> (2.01003341683359 + 1.*y0 + 2.*If[Im[t] == 0 && 1 < t,
UnitStep[20. - 1.*1]*
((0. - 100.*E^(0.01*1) + 100.*E^(0.01*t))*UnitStep[20. - t] +
(122.14027581601698 - 100.*E^(0.01*1))*UnitStep[-20. + t]),
Integrate[E^(0.01*K$73)*UnitStep[20. - 1.*K$73], {K$73, 1, t},
Assumptions -> 1 >= t || Im[t] != 0]])/E^(0.01*t)}}
Steve Luttrell

"Virgil Stokes" <Virgil.Stokes at it.uu.se> wrote in message
news:c6d7q5$jdp$1 at smc.vnet.net...
> Why it this the following so hard for Mathematica 5.0.0
>
>    c[t] = 0.2*UnitStep[20 - t];
>    eqn = y'[t] == 10.0*c[t] - 0.01*y[t]
>    DSolve[{eqn, y[0] == y0}, y[t], t] // FullSimplify
>
> --V. Stokes
>
>


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