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Re: differential equation solve

elvis wrote:
> another equation:
> \!\(DSolve[{\(x'\)[t] == r*x[t] \((1 - x[t]\/xm)\), x[0] == x0}, x,
> t]\)
> this face anothe prolbem

Assuming that the "problem" you faced is the *warning* message returned 
by DSolve, you can easily check that the returned solution is correct:

sol = DSolve[{Derivative[1][x][t] == r*x[t]*(1 - x[t]/xm), x[0] == x0}, 
x, t]

--> Solve::"ifun" : "Inverse functions are being used by (Solve), so 
some solutions may not be found; use Reduce for complete solution 

--> {{x -> Function[{t}, E^(r*t)*x0*(xm/(-x0 + E^(r*t)*x0 + xm))]}}

Simplify[{Derivative[1][x][t] == r*x[t]*(1 - x[t]/xm), x[0] == x0} /. 

--> {True, True}


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