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MathGroup Archive 1998

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Re: Re: help

  • To: mathgroup at smc.vnet.net
  • Subject: [mg15122] Re: [mg15074] Re: help
  • From: Jurgen Tischer <jtischer at col2.telecom.com.co>
  • Date: Sat, 12 Dec 1998 03:59:18 -0500
  • Organization: Universidad del Valle
  • References: <199812100813.DAA04249@smc.vnet.net.>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Ron,
here is what I could make out of it. I supposed your problem is of the
form 

y'[t] + y[t] == 1 - E^t*Integrate[y[tau]/E^tau, {tau, t0, t}]

where t0 is your initial point (that is, known). Then:

In[1]:= eq1 = y'[t] + y[t] == 1 - E^t*Integrate[y[tau]/E^tau, {tau, t0,
t}]; 

In[2]:= eq2 = D[eq1, t];

In[3]:= eq3 = Eliminate[{eq1, eq2}, Integrate[y[tau]/E^tau, {tau, t0,
t}]]

Out[3]= y''[t] == -1

In[4]:= {sol} = DSolve[eq3, y, t]

Out[4]= {{y -> (C[1] + C[2]*#1 - #1^2/2 & )}}

In[5]:= Simplify[eq1 /. sol]

Out[5]= -(1/2)*E^(t - t0)*(t0^2 - 2*t0*(-1 + C[2]) - 2*(-1 + C[1] +
C[2])) == 0

In[6]:= {C2} = Solve[t0^2 - 2*t0*(-1 + C[2]) - 2*(-1 + C[1] + C[2]) ==
0, C[2]]

Out[6]= {{C[2] -> -((-2 - 2*t0 - t0^2 + 2*C[1])/(2*(1 + t0)))}}

In[7]:= sol = sol /. C2

Out[7]= {y -> (C[1] - ((-2 - 2*t0 - t0^2 + 2*C[1])*#1)/(2*(1 + t0)) -
#1^2/2 & )}

In[8]:= Simplify[eq1 /. sol]

Out[8]= True

Jurgen

Ron Gooch wrote:
> 
> yes mathematica based solution is great.  I'm having trouble relating
> this to mathematica.  and help is appreciated.
> 
> Ron
> 
> -----Original Message-----
> From: steve at smc.vnet.net <steve at smc.vnet.net> To: mathgroup at smc.vnet.net
To: mathgroup at smc.vnet.net
> Subject: [mg15122] [mg15074] Re: help
> 
> >Do you want a Mathematica based solution?  If no, post this to
> >sci.math.
> >
> >Moderator
> >
> >> From gooch at ilinkusa.net Mon Dec  7 11:22:40 1998
> >> To: comp-soft-sys-math-mathematica at mail.uu.net
> >> From: "Ron Gooch" <gooch at ilinkusa.net>
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> >> Subject: [mg15122] [mg15074] help
> >> Date: Mon, 7 Dec 1998 10:16:28 -0800
> >> Message-ID: <74gva1$neo at enews4.newsguy.com>
> >> X-MimeOLE: Produced By Microsoft MimeOLE V4.72.3110.3
> >> Content-Length: 118
> >>
> >> can any one solve this eq.
> >>
> >> solve the initial value problem
> >>
> >>  y'(t) + y(t)=1-(integral) e^(t-tau) y(tau)dtau, y(0).
> >>
> >>
> >>



  • References:
    • Re: help
      • From: "Ron Gooch" <gooch@ilinkusa.net>
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