Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).

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3
votes
1answer
1k views

Solve pair of recurrence relations

[Corrected equations and added simple example] Can you solve a system of (loosely) coupled recurrence relations like this in Mathematica somehow? ...
3
votes
1answer
695 views

HarmonicNumber problem

I am looking for all the roots of HarmonicNumber, in the domain [-30, 1] and [0, 6000] for the real and imaginary parts, respectively, and where the parameter ...
2
votes
0answers
52 views

Unusual error message from Solve when called by DSolve

Question 111150 presents an equation nonlinear in its leading derivative ...
2
votes
3answers
3k views

Solve and plot an equation that is dependent on a transcendental equation

I am trying to plot a function that uses the values of a transcendental equation as its input values: y = Tanh[(2 y + x)/2.5] z = 2.5 * Log[2*Cosh[(2 y + x)/2.5]] ...
2
votes
2answers
549 views

Count and plot the number of solutions in an interval

I have equations depending on one or more parameters and I want to find and plot regions in the parameter space in which there is a specific number of solutions. For definiteness let's consider a ...
2
votes
2answers
648 views

Find roots of a function involving Bessel functions

I'm trying to find the roots of a function involving Bessel functions. Here is my code ...
2
votes
1answer
773 views

FindRoot Infinite expression 1/0 encountered error

I have 1 equation in 1 variable, which when I use Plot, looks like this: ...
2
votes
1answer
670 views

How do I get all possible solutions in an underdetermined system? [duplicate]

I have two problems which I'd like to solve with Mathematica. If I have a system of two equations with three unknowns, how can I get to list all possible solutions for the unknowns? Here is what I ...
2
votes
2answers
2k views

Eliminating the Parameter: Transform parametric equation to Cartesian equation and draw arrows along parametric growth

Hey guys I really could use some help on this calc 3 problem. I'm stuck on how to write the code for this problem: a) Eliminate the parameter to find a Cartesian equation for a parametric curve. b) ...
2
votes
2answers
330 views

How do I feed data points into an equation to solve NUMERICALLY?

I start with this equation and solve it numerically for $z(x,y)$ in the range $1 < x < 5$ and $1 < y < 5$: $$ \frac{3}{xyz} - 2x - 3y - 5z = 0 $$ Then using the data points of $z$ above, ...
2
votes
2answers
198 views

How do I get all the roots within a certain range for an equation? [duplicate]

I wish to find ALL the roots of the following equation $ x \tan(ax) - c = 0$ within a range, where a and c are constants I control. I've been using ...
2
votes
2answers
265 views

Solving a system of nonlinear equations 2

Regarding this question: Solving a system of nonlinear equations When I try to solve the same system (with the code proposed in Daniel Lichtblau's answer) with different Right Hand Side values, ...
1
vote
2answers
170 views

How to solve ArcSinh equation for many differents parameters?

I am totally stuck trying to solve the equation below (1/2) x Sqrt[1 + 4 a^2 x^2] + ArcSinh[2 a x]/(4 a) == d Where a and <...
1
vote
0answers
1k views

Solve[] unexpectedly giving empty solution sets for extremely large problems

I was calculating the set of lattice vectors in $\mathbb{Z}^4$ which have taxicab norm $r$. For example, executing ...
1
vote
1answer
676 views

4th-order Runge-Kutta method to solve a system of coupled ODEs [duplicate]

I am a beginner at Mathematica programming and with the Runge-Kutta method as well. I'm trying to solve a system of coupled ODEs using a 4th-order Runge-Kutta method for my project work. I have ...
1
vote
1answer
240 views

Why Integral does not converge?

I am trying to solve for $\Omega$ this nonlinear integral equation: $$1+\dfrac{z}{k^2}-\dfrac{z^2}{K_2(z)} \dfrac{\Omega}{k^3} \displaystyle\int_{1}^{\infty} \gamma^2\, \text{ArcTanh} \left(\sqrt{\...
0
votes
3answers
412 views

Solving a differential equation with mixed conditions using DSolve

I want to solve a differential equation $$ \frac{d}{dx}\left(k_0 \left(\frac{T(x)}{T_0}\right)^n \frac{dT(x)}{dx}\right)=0,$$ with boundary conditions: $T(l)=T_0$, $\;T'(0)=-\frac{q_0}{k_0 T(0)^n}\;$...
0
votes
1answer
929 views
0
votes
1answer
419 views

FindRoot finds a solution not found by NSolve

I am trying to solve a polynomial equation of higher order with non-integer exponents. When the order of the system is greater than 4, FindRoot provides a correct solution that is not found by NSolve. ...
7
votes
3answers
3k views

How to solve an overdetermined system in Mathematica

I would like to understand the reasons and find a way to avoid such behaviour of the Solve function in Mathematica 8. ...
7
votes
1answer
251 views

How to plot inequalities taking into account that points must be integers and not reals?

I have solved with Mathematica 9 the following integer inequalities using Reduce: ...
6
votes
3answers
449 views

Why don't I get numeric values from this Solve?

Solve[ a^2 + b^2 == c^2 && a < 100 && b < 100 && c < 100, {a, b, c}, Integers] gives me this result ...
6
votes
2answers
388 views

NSolve missing solutions in Mathematica 10

Running Mathematica 8.0.4 and 10.0.0 on a Windows 8.1 machine. Processed the same code with both kernels: ...
6
votes
1answer
175 views

Why is FindInstance failing when I relax a set of constraints?

I'm attempting to use FindInstance to generate coordinate sets for plausible triangles with edge length distance constraints. E.g.: ...
6
votes
3answers
881 views

Arithmetic operation on the value returned by Solve

I want to modify the value that is returned by Solve. Example: SolC1 = Solve[Sin[ π x / L] == 1, x] {{x -> L/2}} I need to add n to x so that x becomes ...
5
votes
2answers
184 views

Reduce applied to vectors doesn't work right?

Reduce[{x,0}=={0,0}, x] gives x==0 as it should, but Reduce[{x,0}!={0,0}, x] gives False, which indicates no solution ...
5
votes
1answer
185 views

$x^6-2\varphi^5x^5+2\varphi x+\varphi^6=0$ solving in radicals

How to solve the equation $x^6-2\varphi^5x^5+2\varphi x+\varphi^6=0$ in radicals using Mathematica? where $\varphi$ is the golden ratio. Solution is Ramanujan's Class Invariant $G_{125}$, Class ...
5
votes
1answer
92 views

Passing starting values to FindRoot when called by the Shooting Method of NDSolve

According to the documentation of the NDSolve Method -> "Shooting" option, it is possible to pass to ...
5
votes
3answers
246 views

Finding the conditions for degenerate solutions to a cubic equation

I have a cubic equation (corresponding to the band structure of a physical system) given by w in the code below. ...
5
votes
2answers
439 views

Equation solving with GroebnerBasis

I have a system of quadratic equations defined below ...
5
votes
2answers
351 views

DSolve returns a “wrong” solution

This wrong solution exists from mma9 to mma10.1: ...
4
votes
1answer
606 views

What algorithms does NSolve use?

I've been using NSolve to find roots and now I've been wondering what underlying algorithm Mathematica uses. It's probabaly similiar to ...
4
votes
4answers
2k views

recursively solve equation and saving the values

I am new to Mathematica. I am trying to recursively solve an equation and saving the values into a Table. Since I need the real solutions only I use ...
4
votes
1answer
789 views

Tips for efficiently solving large system coupled (nonlinear) ODEs

I'm trying to solve a system of nonlinear, coupled ODEs, where the governing equation for the $n$-th ODE is of the form: $$\sum_k^M Q_{nk} \ddot{a}_k -\sum_{\ell}^M\sum_k^M S_n(\ell,k) \dot{a}_{\ell}...
4
votes
0answers
78 views

Method of characteristics, recursion formulas

I'm helping a friend out with a problem. He needs to plot out the solution to a water surge in a pipeline. I have all the parameters set and I've put the equations in Mathematica, but I can't get the ...
4
votes
1answer
203 views

Finding the largest integer that cannot be partitioned in a certain way

I want to use Mathematica to solve the problem: Find the maximum $k$ such that $6x+9y+20z=k$ does not have a non-negative solution. I tried FrobeniusSolve. ...
4
votes
1answer
104 views

Does Solve[] find ALL the exact roots of rational polynomials?

Does Solve[] find ALL the exact roots of rational polynomials? I've done a bunch of tests where I created an expression with some analytic roots, and Solve[] always found them all. But is the ...
4
votes
3answers
328 views

FindRoot constrained to maximum

I am using FindRoot to find the local maximum op some function, by examining where its derivative is zero. However, keeping the starting value the same, sometimes <...
4
votes
2answers
835 views

Solving a linear equation in Mathematica

This should be easy but I can't seem to find the right way to do it. I have an equation of the form $a x + b x + c y + a z + d z = 0$, and I'd like to solve for relations between the parameters $a,b,...
3
votes
2answers
379 views

How to solve numerically an equation which contains numerical intergration?

F1[x_] := NIntegrate[E^Sin[y x], {y, 0, 1}] F2[x_] := Log[x] NSolve[F1[x] == F2[x], x] I want to solve the equation, but Mathematica don't solve it. ...
3
votes
2answers
95 views

Switching between solutions of a fourth order polynomial

I am plotting the roots of a fourth-order polynomial as a function of some parameter $r$ with the following code: ...
3
votes
1answer
218 views

Aborts and beeps without error warning

I have a piece of code that generates a figure, performing a calculation to generate each pixel. At a certain resolution it runs fine, but after a high enough resolution it fails. Mathematica beeps (...
3
votes
2answers
107 views

Evaluating Functions on Zero Sets (of other functions)

I have a highly non-trivial function, call it $f(x,y)$, in which I want to look at its zero set in the $(x,y)$ plane, and plot/evaluate a different function $g$ precisely along this zero set. I have ...
3
votes
3answers
319 views

Solve: Merging two branches of the solution

I have the following code: ...
3
votes
1answer
129 views

Computing planet conjunctions with 2D circular orbits still hard?

All methods I've seen for computing planetary/stellar conjuctions (when two planets or a planet and a star appear close together in the sky because their angular separation, as measured from Earth, ...
3
votes
3answers
485 views

Animate a position change along the curve for every iteration

I've only had few previous experiences on Mathematica before. So basically an entry-level question that harasses a rookie like me. I made the following attempt using bisection method to calculate ...
3
votes
1answer
115 views

How to solve coupled multi-variable polynomials?

The following code generates two polynomials $q_1$ and $q_2$ in complex variables p and c: ...
3
votes
2answers
261 views

How can Mathematica help me to find a real radical expression for roots of this polynomial?‎

The polynomial $P(x)=x^‎‏4‏‎-‎‏4‏x^‎‏2‏‎-‎‏2‏x+‎‏1$‏‎ has ‎‏4‏‎ real roots (this can be clearly checked by plotting). But solving $P(x)=‎‏0‏‎$, using ...
3
votes
1answer
85 views

Solving a list of equation which takes so much time

I try to solve a list of equation in a following way but it Mathematica solves equations after 30-40 minutes or don't solve them at all. The functions that I use are ; ...
3
votes
1answer
462 views

Solution given by Wolfram Alpha but not _Mathematica_

Why will Mathematica not give a soluion to Solve[Log[x] == Log[j, Log[j, x]], j], but Wolfram Alpha will?