Re: [Q] Differential equation?
- To: mathgroup at smc.vnet.net
- Subject: [mg22640] Re: [Q] Differential equation?
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Thu, 16 Mar 2000 09:10:55 -0500 (EST)
- Organization: Universitaet Leipzig
- References: <8an28e$1u9@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi James, you can solve this equation with Mathematica a) reduce it to a second order equation for y[1][t] deqn2=y[1]''[t] + (a + b - c*t)*y[1]'[t] - (c + a*c*t)*y[1][t] ==0 b) remove the first derivative with deqn3 = (deqn2 /. Thread[{#, D[#, t], D[#, t, t]} & /@ (y[1][t] -> Exp[Integrate[-a - b + c*t, t]/2]*u[t])] // FullSimplify) /. (g_Power*f_Plus == 0) :> f == 0 gives (a^2 + 2*c + (b - c*t)^2 + 2*a*(b + c*t))*u[t] - 4 u''[t] == 0 hmm - something hypergeometric fine, let's try DSolve[] DSolve[deqn3, u[t], t] // FullSimplify and get {{u[t] -> (((a - b + c*t)^2)^(3/4)* (C[2]*Hypergeometric1F1[(3 + Sqrt[c^(-2)]*(2*a*b + c))/ 4, 3/2, (Sqrt[c^(-2)]*(a - b + c*t)^2)/2] + C[1]*HypergeometricU[(3 + Sqrt[c^(-2)]*(2*a*b + c))/4, 3/2, (Sqrt[c^(-2)]*(a - b + c*t)^2)/2]))/ (2*E^((Sqrt[c^(-2)]*(a - b + c*t)^2)/4)* (-(c^2*(a - b + c*t)^2))^(1/4))}} It is up to you to revert the transformations. Hope that helps Jens James wrote: > > Hi! > > I began to use Mathematica, and found out it is great. > But I happen to have a question during solving differential equtations. > Here's a problem. > > y'_0(t) = -a * y_0(t) + b * y_1(t) > y'_1(t) = a * y_0(t) + (c*t-b) * y_1(t) --- (*) > ^ > This can be solvable mathematically, even some tedious work, > but when I use Mathematica, it can't solve it. > After some trial and error, I found out that 't' in (*) > is the problem - problem that mathematica doesn't give an answer, > it just shows the above equations as an answer. > So I wonder if this is the limit of Mathematica, > or is there any way to solve it? > I sincerely hope there's some way - because my work involves > a lot of Diffrential Equations. > Any reply would be appreciated. > > James.