Re: [Q] Differential equation?
- To: mathgroup at smc.vnet.net
- Subject: [mg22633] Re: [mg22620] [Q] Differential equation?
- From: "Mark Harder" <harderm at ucs.orst.edu>
- Date: Thu, 16 Mar 2000 09:10:49 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
James, I tried solving your eqns and got the same result -- mathematica just returns the input line DSolve[ {...., ....},{y0[t],y1[t]},t ]. Inspecting the equations, I noticed that there are some dependencies between them -- the sum of the 2 eqns, y0'[t]-y1'[t] == b y1[t] - (c t -b) y1[t] doesn't involve y0[t] at all! Also, what if c=0? So I changed the equations somewhat a=2; b=1; c=3; d=4; eqns2= {y0'[t] == -a * y0[t] + b * y1[t], y1'[t] == c * y0[t] + (2*t-d) * y1[t] }; so that the matrix of the equations is full-rank. Now DSolve[eqns2,{y0[t],y1[t]},t] returns something so ugly, I won't try to print it; but it looks like expressions for y0 and y1 in terms of integrating factors that are exponentials of integrals of expressions in Bessel I functions (try it yourself). At least, its a solution. I know mathematica is very fussy about returning solutions requiring unstated assumptions to be valid, and I think that is part of your problem. Try defining the problem a little more carefully, and it may be that if the coefficients of y0[t] have to be negatives of each other, then the equations are not soluble. -mark -----Original Message----- From: James <research at proton.csl.uiuc.edu> To: mathgroup at smc.vnet.net Subject: [mg22633] [mg22620] [Q] Differential equation? > >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. > >