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May
20
comment Solar System Orbital Parameters
Just in case you are interested in accuracy, it might be worth noting that the system of ODEs described in your previous question at mathematica.stackexchange.com/questions/25039/… is not what is usually meant by an "n-body simulation," because it does not account for interactions among the bodies: it's just a collection of independent central field solutions. It might be a fine approximation for times close to the initial time but will be observably incorrect.
May
20
comment Find all the integer numbers $a$, $b$, $c$, $d$, $e$, $f$, $k$ to this equation have three integer different solutions?
The question, which evidently is missing several words, now reads as if you are asking for all integral values of $a,\ldots,k$ in the interval $[-10,10]$ for which your equation has three distinct integral solutions. Is this a correct interpretation?
May
18
reviewed Close Generating a list of all factorizations
May
18
reviewed Leave Open Strange Behavior of NDSolve
May
18
reviewed Leave Open Doing vector manipulations on Mathematica
May
18
comment Using single replacement rule to convert algebraic expression
You might find Alternatives to be useful.
May
17
comment Solving an ODE in power series
+1 This is a good start. Power series solutions, though, are frequently used to obtain recursion equations for the coefficients (of any solution that might be analytic within a neighborhood of the point of expansion). It would be nice, then, to have a function that outputs these equations (given a differential operator as input), rather than just obtaining an approximate solution with a limited radius of accuracy. In order to analyze singular points, it would also be useful to consider slightly more general series of the form $z^\alpha(a_0+a_1z+a_2z^2+\cdots)$ for non-integral $\alpha$.
May
16
reviewed Close How to tell Mathematica to make assumptions?
May
16
reviewed Leave Open Using ImageTransformation[] with a lookup table
May
16
reviewed Close List of Tribonacci Polynomials with Mathematica?
May
15
comment Integration of a rational function
Alternatively, use the Residue Theorem. Implicitly assuming $b\gt 0$ (WLG) and $c\gt 0$, we may (very quickly) obtain the solution as 2 \[Pi] I Sum[Residue[(a + x)/((b^2 + (a + x)^2) (1 + c (a - x)^2)), {x, z}], {z, {b I - a, I/Sqrt[c] + a}}] // Simplify, yielding $\frac{2 a \sqrt{c} \pi }{1+2 b \sqrt{c}+4 a^2 c+b^2 c}$.
May
15
revised How to deal with zero in NDSolve in mathematica?
added 94 characters in body
May
15
comment How to deal with zero in NDSolve in mathematica?
That completely changes the question!
May
15
comment How to deal with zero in NDSolve in mathematica?
+1 This argument can be made rigorous by considering the approximate differential equation as a perturbation of the original. Applying DSolve with initial conditions is not very persuasive. It's more insightful to omit initial conditions: the solution will include a Bessel function of the second kind. This captures the singular behavior at the origin and approximates the singular behavior of the original equation there, too. Standard theory shows that's all the solutions you can have--just two dimensions of them--and then the rest of the analysis goes through as shown here.
May
14
comment How to deal with zero in NDSolve in mathematica?
The equations are inconsistent with the initial conditions. At $t=0$ you are requiring that $0 = t y'(t) = -x(t) - t \exp(x(t)) = -1$ which is impossible.
May
14
reviewed Reviewed Variable naming changes everything
May
14
reviewed Leave Open How to store a SparseArray?
May
14
awarded  Enlightened
May
14
awarded  Nice Answer
May
11
awarded  Good Answer