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 ...


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