# Problem evaluating results of DSolve (Power::infy)

So, after browsing through older posts to see if anybody else could have had the same problem, I have come to the conclusion that I am stuck. That bothers me, especially because it should be straight forward.

I am trying to solve a Differential Equation. The equation is:

I would like to find X(t), and hence plot X as a function of time. It is known that X = 0 when t = 0.

I write this the following way:

solOpg13a1 =
DSolve[{D[X[t], t] == (k*(1 - X[t])*(t*Fa - X[t]*nB0))/(V0 + t*v0), X[0] == 0}, X[t], t];


Next, I prepare it for plotting by the following:

eqOpg13a1 = X[t] /. solOpg13a1 //. {k -> 5.1 , V0 -> 1500 , nB0 -> 1125 , Fa -> 6.0, v0 -> 4} // First;


Please note that V0 and v0 are not the same.

X(t) works OK for values above 150 (more or less). For values of t less than around 150, I get a series of Power::infy and Infinity::indet errors.

It should be straight forward, and so I am sorry to call for help, but I just can't put a finger on where I go wrong.

The time to t_full is approximately 250 Hours (which is the unit of t). I am using Mathematica 9.

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I think it's just an issue of balancing big numbers. This will work : aux[t_] = FullSimplify[ X[t] /. First@ DSolve[{D[X[t], t] == (k*(1 - X[t])*(t*Fa - X[t]*nB0))/(V0 + t*v0), X[0] == x0}, X[t], t]], sol[t_] = FullSimplify[ aux[t] /. {x0 -> 0., k -> 5.1/100, V0 -> 1500, nB0 -> 1125, Fa -> 6, v0 -> 4}] and then plot/use sol[t]. – b.gatessucks Nov 3 '13 at 18:53
I also found out the problem can be solved by usingNDSolve instead, for the range {t,0,250}. This gave the plot that I was expecting. – Simon P Nov 3 '13 at 18:54
The laziest of all approaches :D Plot[X[t] /. FullSimplify@sol /. {x0 -> 0., k -> 5.1/100, V0 -> 1500, nB0 -> 1125, Fa -> 6, v0 -> 4}, {t, 0, 300}] produces this plot of the solution. – Sektor Nov 3 '13 at 19:07

Plot[X[t] /. FullSimplify@sol /.