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>