4
The OP seems maybe to want X as a function of x, but the OP gives up an equation that defines X as a function of t. No good clue about how to incorporate x into the solution X[t] as defined by the given equation.
Here's one way to go about finding X[t] numerically. The equation has a 3-parameter family of solutions, so we seek an order-3 differential ...
3
Mathematica cannot solve your equation for X .
Instead try to solve it for t
sol=Solve[X (X - a) + b Exp[-2 X t] == B, t ][[1]] /. C[1] -> 0(*forces real solution*)
(*{t -> Log[b/(B + a X - X^2)]/(2 X)}*)
Now you know t as a function of X.
For examplary parameters you can plot the result
ParametricPlot[{t, X} /. sol /. {a -> 1/5, b -> 1, B ->...
2
To find the closed-form use RSolve
Clear["Global`*"]
t[n_, x0_] =
x[n] /. RSolve[{x[n] == 11/10 x[n - 1], x[0] == x0}, x[n], n][[1]]
(* (11/10)^n x0 *)
The initial sequence is
t[#, 10.] & /@ Range[0, 5]
(* {10., 11., 12.1, 13.31, 14.641, 16.1051} *)
For an arbitrary term
t[1000, 10.]
2.46993*10^42
Alternatively, starting with an ...
Only top voted, non community-wiki answers of a minimum length are eligible
