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Computer. pentools. | jedi_mps. Yola. site.Q: Differential equations with known analytic solutions but unknown (?) numerical solutions I am currently trying to relate a discrete time system: $$x_{t+1} = e^{ -x_{t}}x_{t} \qquad x_{0} = 1$$ with a differential equation: $$x'(t) = a - bx(t) \qquad x(0) = 1$$ where a and b are known but unknown in the general case (even though they both range over 0 to +infinity). Doing a bit of searching, there seems to be a way of doing this in terms of Laplace transforms: $$\frac{X_t}{X_{t-1}} = \frac{bX_{t-1}}{X_{t-1}-b}$$ $$X_{t} - X_{t-1} = bX_{t-1}$$ $$X_{t} = X_{0}e^{\frac{bt}{1-b}}$$ I'm wondering what the general solution (so far, I just have the system and differential equation) in this case might look like? Note that there may be more than one solution. A: I do not think you can get anything analytically: this is a linear differential equation with general coefficient $b$. There is no known general method to solve such equations (except the standard method of solving first order equations). I suggest that you try to write it for the discrete-time model and see what you get. Edit: From the revised question, you get the following finite difference equation for the discrete-time model: $$x_{t+1} = \frac{a}{e^x_t}x_t.$$ Let $y_t = e^x_t$, so that the original equation becomes $$x_{t+1} = \frac{a}{y_t}.$$ The size of the matrix in the discrete-time model will be $n = n(n_0)$, where $n_0$ is the number of iterations since the starting point. Edit: Let me make another remark concerning the difference between the differential equation and the discrete-time one. In your discrete-time model there are

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