HELP! Why are the solutions from NDSolve and DSolve not identical?

[Loling Song]

I have, what I believe, a system of two linear, first-order,
inhomogeneous differential equations describing a real biological
system. When I tried to solve this system for a numerical solution by
NDSolve, it gave a solution that was different from that of the
symbolic solution (in which I used the same boundary conditions).

NDSolve[{y1'[t] == a y1[t] + b y2[t], y2'[t] == d + c y1[t] - b y2[t],
y1[0] == 0.0018, y2[0] == 0.03}, {y1[t], y2[t]}, {t, 0, 18000},
MaxSteps -> 1000000, AccuracyGoal -> 10, PrecisionGoal -> 10,
WorkingPrecision -> 20]

DSolve[{y1'[t] == a y1[t] + b y2[t] , y2'[t] == d + c y1[t] - b y2[t]
}, {y1[t], y2[t]}, t]

I am puzzled by these results, and would very much like to arrive at an
analytical solution. I would very much appreciate ideas and
suggestions to help me get there.

Many thanks in advance.

Loling Song
Cornell University
Department of Physics,
117 Clark Hall,
Ithaca, NY 14853

Email: LS...@cornell.edu

[Jens-Peer Kuska]

Hi,

NDSolve[] gives a numerical approximation to the solution.
DSovel[] give the solution of the differential equation.
An approximation must be different from the true solution
otherwise it is not a approximation.

As long as you don't give the full input, i.e., the paramters
a,b,c,d we can't tell you what's wrong with your numerical
solution and why it differs so much from the analytical
solution.

Regards
Jens