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
908 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? ...
2
votes
2answers
203 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, ...
2
votes
2answers
239 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
1answer
1k views

Solving Heat equation [closed]

I want to compute the exact solution of the heat equation but I got an error. u(x,t) (equation of transmition of heat) is the solution of this differential equation: $$du/dt - \alpha d^2u/dx^2 = 0$$ ...
2
votes
3answers
2k 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
416 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
1k views

Why doesn't Mathematica solve $x=\cos\,x$ properly? [duplicate]

Why doesn't Mathematica solve x == Cos[x] properly? Both Solve and NSolve fail with the ...
1
vote
2answers
125 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 ...
0
votes
1answer
177 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. ...
0
votes
1answer
647 views
-3
votes
2answers
106 views

Solving the symbolic quadratic equation ax2 + bx + c = 0 [closed]

I need to ask Mathematica to solve the symbolic quadratic equation ax2 + bx + c = 0. Does it give you the right answer?
7
votes
1answer
221 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
4answers
142 views

How to eliminate variables when using Solve[]

In certain problems, we need to solve systems of equations and get results in terms of just selected variables. For example, how could we solve eqn==0 below for ...
6
votes
1answer
162 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
412 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
3answers
746 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
384 views

Equation solving with GroebnerBasis

I have a system of quadratic equations defined below ...
4
votes
2answers
286 views

Why doesn't Roots work on a certain quartic polynomial equation?

In everything that follows I am using Roots to get the solutions to the equations. I start off with this equation: $$ \frac{A}{3}x^4 - x^2 + 2ax - b^2 = 0$$ Now ...
4
votes
2answers
512 views

Why doesn't FindRoot work correctly?

I'm trying to find the roots of the following equation: I need to find λs for different values of ξ. I know that for all ...
4
votes
4answers
1k 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 ...
3
votes
2answers
297 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
1answer
219 views

Issue in ParallelTable after evaluating another function using NDSolve and FindRoot. What is wrong with this inverse?

I am trying to find the inverse of a function which is defined through NDSolve and NIntegrate. The question is pretty similar ...
3
votes
1answer
128 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
1answer
192 views

Strange behavior of Reduce with a cubic equation

This equation: $(\frac{-a}{x})^2=\sqrt{\frac{1}{x}}$ at $a > 0$ and $x > 0$ has a clear solution $x=a^{4/3}$, doesn't it? However, ...
3
votes
1answer
489 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} ...
3
votes
3answers
213 views

Speed up Eliminate

I have a set of trig equations, c1,c2,c3 are constants, I excepted the result is c1 c2 c3 r^2 + (c1^2 + c2^2 + c3^2 - 1) r + c1 c2 c3 == 0 but following code ...
3
votes
1answer
187 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. ...
3
votes
1answer
216 views

How can I get the general term of this recurrence equations?

Following is the recurrence relation: a[1] = 1; a[n_] := a[n - a[n - 1]] + 1 Array[a, 28] I tried to use RSolve, but it ...
3
votes
1answer
715 views

Linear Solve with Modular Arithmetic

I am interested in using LinearSolve[m,b] which will find a solution to the equation $m.x=b$, where I am in mod 2 arithmetic. Is there any way to perform this ...
3
votes
1answer
534 views

wrong use of _?NumberQ?

I am having trouble with a numerical exercise. Here's a simplified version of my problem. I define two functions to find the solution to two constrained maximization problems: ...
3
votes
3answers
429 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 ...
2
votes
3answers
281 views

Points of Intersection

How to numerically find points of intersection between pair of curves (Here,a circle and a parabola) ? Finding it a bit messy as, for a point on one curve, slope of the other is involved. ...
2
votes
1answer
162 views

Catastrophic loss of precision

while I am trying to solve the double integral in the range of 0 to Infinity (for both the integral) it give me the error Catastrophic loss of precision in the global error estimate due to ...
2
votes
2answers
180 views

cycloid parametric [closed]

How do I enter 3 parametric equations for cycloids corresponding to circles with radii 1, 2, and 4. I have tried ...
2
votes
1answer
313 views

Solving a system of nonlinear equations

The bellow set of equations has two answer sets for (α1, α2, α3, β1, β2, β3) respectively as following: (3, 1, 3, 1, 1, 1) & (3, 0.75, 3, 0.5, -1, 0.5) ...
2
votes
1answer
76 views

Find constants in a function? [closed]

Let's say I have a function f[x] with n constants, e.g. f[x] = c1 * x + c2*x^2 + ... + cn *x^n I also have n conditions to find those constants, e.g ...
2
votes
2answers
158 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 ...
2
votes
3answers
150 views

Solve works with numbers but not number stored in variable

I have the code: ...
2
votes
3answers
231 views

Is there a way to specify custom domains?

I want to solve for all solutions to the system of equations $a_1 a_2 a_3 b_4 + a_1 a_2 b_3 + a_1 b_2 + b_1 = 0$ and $a_1 a_2 a_3 a_4 = 1$ where the $a_i$'s and $b_i$'s take on values from $\{-1,1\}$. ...
2
votes
1answer
519 views

Solve[Tan[theta] == (b*Sin[t])/(a*Cos[t]), theta] breaks when “Reals” is added?

Mathematica solves this equation fine: Solve[ Tan[theta] == (b*Sin[t])/(a*Cos[t]), theta] // InputForm ...
2
votes
1answer
130 views

Compact form for domain ranges of many variables

When one sets up an equation to solve one often needs to specify conditions on the variables such as { x>0 && y>0 && z>0 } This is not ...
2
votes
1answer
854 views

How could I define a function as the solution of equations in Mathematica?

I have posed a specific question yesterday but it may be too trivial to answer. I think the question could be asked in a more general way so it is easier to answer. Then I could solve the original ...
2
votes
1answer
162 views

Finding the root of a nested function with small values

I have reduced an error in my program to this line of code: FindRoot[Nest[# (1 - #) k &, 1/2, 2^4] - 1/2, {k, 3.5}] It works for $2^1, 2^2, 2^3, 2^4,$ but ...
2
votes
1answer
139 views

How to transform an expression using algebraical instead of pattern rules [duplicate]

I would like to transform rules algebraically. A very simple example would be: - k^2 - 2 k x + x^2 /. {2*k -> 1} This transforms to: - $$k^2-2 k x+x^2$$ ...
2
votes
2answers
497 views

FindRoot errors

I'm trying to solve a system of two equations in two variables for some range of parameter values. I use ContourPlot to see where I should look for a solutions and ...
2
votes
1answer
956 views

'not a valid variable' error when trying to solve 13 equations with 13 variables

I want to solve 13 variables by 13 equations. And here is my program: ...
2
votes
1answer
639 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
478 views

Inconsistent initial and boundary conditions

I have a 4th order nonlinear PDE with the following BCs and IC: ...
1
vote
1answer
72 views

How to speed or help Solve[] when it is stuck?

The code below generates a system of equations that I need to Solve[] for {c[5], c[6], c[7], c[8]} in terms of {c[1], c[2], c[3], c[4]}. ...
1
vote
1answer
99 views

Solving ODES in order to find unknown constants

I am trying to solve a set of ODES which represent a second order consecutive chemical reaction. ...