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

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1
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0answers
441 views

Calculating the mean curvature of a surface - suggestions

I am attempting to calculate the mean curvature [1, 2] of a surface defined by a function of x and y. My function is rather ...
0
votes
1answer
175 views

x/.NSolve[f==g,x] does not work when f or g is the output of NDSolve!

I have been trying to put Points at the intersection of two curves, one of which is the ouput of a differential equation solved with NDSolve. The output being an Interpolation, NSolve cannot find the ...
3
votes
1answer
457 views

How to solve this equation with positive integers as a solutions?

This is a problem of United Kingdom Mathematical Olympiad. Find all triples $(x,y,z)$ of positive integers such that $$\biggl(1+\dfrac{1}{x}\biggr)\cdot \biggl(1+\dfrac{1}{y}\biggr)\cdot ...
11
votes
2answers
700 views

NSolve gives additional solutions that don't satisfy the equations!

I am trying to solve the following polynomial equations in Mathematica: ...
1
vote
1answer
209 views

How to find 4 unknowns?

There are 4 unknowns constants: a,b,c,p. The variable is ...
0
votes
0answers
152 views

Reducing a statement with Mathematica, step by step [duplicate]

Possible Duplicate: Get a “step by step” evaluation in Mathematica I have a list of inequalities combined with quantifiers. And Mathematica is able to reduce to simple statement with the ...
6
votes
3answers
358 views

Plotting $\omega(k_x, k_z)$ in $(\omega, k)$ plane with assumption of $k^2 = k_x^2 + k_z^2$

I'm currently studying atmospheric-gravity waves and their dispersion relations. For analysis I need to plot the dispersion function: \begin{equation} \omega^4 - \omega^2\cdot C_s^2(k_x^2 + ...
8
votes
2answers
1k views

How do I work with Root objects?

I want to solve the trigonometric equation : $$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$ I tried Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x] It returns the ...
2
votes
1answer
322 views

How to solve this exponential inequality?

I want to solve the exponential inequality $$8^x +18^x -2\cdot 27^x>0.$$ I tried Solve[8^x + 18^x - 2*27^x > 0, x] and ...
1
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0answers
89 views

Symbolic FindInstance

I'm wondering if there is any way of doing something like the following: FindInstance[x < y, {x}, Reals] and getting, as a possible return value, ...
0
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0answers
601 views

Reduce/NSolve cannot solve a constraint problem?

I am trying to solve the following problem: Minimize Integral[ (y''[x]+10)^2,x] Where y''[x]+a*y'[x]+y[x] = 0, and the initial conditions for the DE are ...
2
votes
2answers
815 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 ...
5
votes
4answers
1k views

How to solve this logarithmic equation?

The equation $$x^2\cdot\log_2\dfrac{3+x}{10}-x^2\cdot\log_{\frac{1}{2}}(2 + 3x)=x^2 - 4+2\cdot\log_{\sqrt{2}}\dfrac{3x^2+11x+6}{10}$$ has two solutions for x, namely 1 and 2. I tried ...
1
vote
1answer
106 views

How to find the values of $m$ so $A \cap B = \emptyset$ and $A \cup B = (-3,+\infty)$?

I have two intervals $A = (-3, m^2- 2]$ and $B=[m, +\infty)$. How to find the values of $m$ so that $A \cap B = \emptyset$ and $A \cup B = (-3,+\infty)$? I tried ...
3
votes
0answers
769 views

Solving a system of nonlinear equations self-consistently

I am trying to solve a set of three non-linear equations in Mathematica. I need help with them. The Mathematica code (in plain text format) is attached below. If you copy & paste the code below ...
1
vote
1answer
345 views

Using 'Reduce' to solve a set of inequalities, specified by a list

I have a two lists $LHS$ and $RHS$, both of size $n$. I want to solve a system of inequalities of the form: $$LHS[1] \leq RHS[1]$$ $$LHS[2] \leq RHS[2]$$ $$LHS[3] \leq RHS[3]$$ $$\vdots$$ ...
2
votes
1answer
294 views

Vector Analysis: Why are the Grad, Laplacian and Div being evaluated to zero

For the non linear partial differential equation below, why are the Gradient, Laplacian and Divergence being evaluated to zero despite using the VectorAnalysis ...
3
votes
1answer
933 views

Finding the Minimum value of an interpolating function

I can't seem to use FindMinValue to find the min. value of a curve represented by an interpolating function. For instance the below code generates an interpolating ...
1
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1answer
343 views

2 non-linear equations with 2 unknowns which I cannot solve

I have the following equations and I would like to solve them in Mathematica anyway. Numerical results are very much welcomed. However, when I use the command ...
2
votes
1answer
511 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
494 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 ...
-1
votes
1answer
582 views

Help to solve Simultaneous Equations

I think this should be easy to numerically solve in Mathematica, but for some reason I'm not finding the correct way to do it. I basically want to solve these simyltaneous equiations: ...
0
votes
1answer
198 views

FindRoot on a 2D list of Equations

I have a $n \times k$ Matrix of data that I want to feed into an equation and solve for an unknown variable. I suppose I can always just convert the Matrix into a long Array but I'd like to learn how ...
2
votes
1answer
268 views

Defining regions for `Exclusions`

I have the following function I want to plot in 3D (For simplicities sake we can say $a=5,b=-1,c=3$.) ...
10
votes
1answer
731 views

How do I find all the solutions of three simultaneous equations within a given box?

Sometimes, one needs to find all the solutions of three simultaneous nonlinear equations in three unknowns $$\begin{align*}f(x,y,z)&=0\\g(x,y,z)&=0\\h(x,y,z)&=0\end{align*}$$ within a ...
3
votes
1answer
180 views

Tracking FindRoot errors in NestWhileList and Table

I'm solving many systems of two equations by varying the initial parameters. I'm running FindRoot in a NestWhileList where the ...
2
votes
1answer
343 views

How to solve simultaneous equations faster with Compile?

I have large 6x6 matrix Uwhich is a multiplication of 15 rotational matrix. All of the elements are Sin\[theta] and ...
1
vote
3answers
338 views

equation solving problems

I have some equation: $$ veq=-2-lr-l^2r+2(r+ir^3\omega) v' + (-2+r)r^2v'^2 + (-2+r) r^2 v''==0 $$ or in Mathematica form: ...
6
votes
2answers
336 views

Reduce and Solve unable to solve equation

I have the following equation. Why aren't Solve and Reduce able to find the solution? ...
1
vote
2answers
298 views

Replacing variable in an equation with an Interpolating function polynomial and plotting residual

I was trying to plot the residual for the solution of my PDE. However, I was unsure about a couple of things. I imported the data and created an Interpolation polynomial with ...
3
votes
2answers
398 views

Is there a way to solve the Apollonius Circle problem in Mathematica?

Assuming x, a, and b are complex numbers, is there a way to reduce the equation Abs[x - a] == k Abs[x - b] to something like ...
5
votes
2answers
1k views

Solving a trig equation

I am trying to find an explicit solution to a trigonometric equation. It is running for a long time and I didn't get any result, but Maple solves it quickly. Why ? ...
3
votes
1answer
489 views

Solving Simultaneous Equations

I am trying to solve two equations that take the form: $W_0 \sqrt{1+\left(\dfrac{z}{\lambda\,\pi\, W_{0}^2}\right)}=W_1\;\,\quad \ldots(1)$ $W_0\sqrt{1+\left( \dfrac{z+0.1}{\lambda\, \pi\, ...
2
votes
1answer
259 views

How to solve a symbolic equation with symbols in powers

I am trying to solve $\dfrac{\rho\ ((1-b)\ \lambda _f\ \lambda _s\ P _A)^{\rho }}{b-1}+\dfrac{\rho \left(\dfrac{b\ \text{ps}\ x}{1-\text{ps}}\right)^{\rho }}{b}=0$ in terms of $b$, I ...
0
votes
1answer
185 views

How to solve this equation? [closed]

The numbers real x and y, are solutions of the following equation system : $$ \{x^3 + 3x^2y + 3xy^2 + y^3 2\sqrt2$$ $$ \{x^3 - 3x^2 + 3xy^2 -2y^3=0 $$ . $$ x^2 + y^2$$ How to solve it ?
4
votes
1answer
590 views

Reduce an equation by putting a new variable

I have the following equation given: $$ (26-x)\cdot\sqrt{5x-1} -(13x+14)\cdot\sqrt{5-2x} + 12\sqrt{(5x-1)\cdot(5-2x) }= 18x+32. $$ In order to solve it, I want to substitute $t = \sqrt{5x - ...
15
votes
1answer
567 views

Why does repeating an equation help in FindRoot?

I'm trying to understand this behavior of FindRoot. Consider a sample function (the one I'm actually interested in is far more complicated, but has similar issues) ...
0
votes
1answer
310 views

(N)Solve does not solve equation

I am trying to calculate where a beam hits a mirror. The mirror is described by this curve (two facing spherical mirrors): ...
5
votes
2answers
232 views

Solve for $a$ as a function of $\beta$?

I am trying to solve this equation: $$\beta^{-a} \Gamma(a) \sin(a \pi) + e^\beta \beta^{2 a - 1} \Gamma(1 - a) \sin(a \pi) = 0$$ I tried the following: ...
0
votes
1answer
247 views

Iterative way to find roots of confluent hypergeometric function

I am trying to find roots of confluent hypergeometric function and I wonder if I can choose the initial guess by the choice of $\beta$. ...
11
votes
4answers
467 views

How to make a Line[] with no end?

I'm trying to do this: In this graph, the secant points are aproximated in order to become the tangent, it seems I need some kind of function which plots a line based on two points and it's points ...
1
vote
1answer
371 views

Using previous two solutions as a start point in FindRoot

I need to solve a sequence of equations and I want the starting point of each new FindRoot to be the solution of the earlier FindRoot, increased or decreased by a a bit in the following way: Some ...
7
votes
3answers
925 views

Finding the number of solutions to a diophantine equation

I want to count total number of the natural solutions (different from 0) of the equation $2x + 3y + z = 100$, but don't know how. How can I calculate it using Mathematica? I tried: ...
23
votes
3answers
6k views

Marking points of intersection between two curves

I'm trying to illustrate the solutions numerically and graphically for an equation such as Tan[x] == x. I think I did everything ok except I wanted to mark each ...
3
votes
1answer
336 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: ...
6
votes
3answers
350 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 ...
1
vote
1answer
613 views

FindRoot inside Table

(MWE at the end of the post) I need to solve a non-linear equation $f(y;x_1,x_2,..,x_5)$ in one variable $y$ and then compute 4 new output expressions, for over 60 different initial parameter inputs ...
4
votes
2answers
564 views

How can I solve the equation with integers as a solution?

I want to solve the equation $$(x-1)^2 + (y-1)^2 + (z-1)^2 = 49$$ where $x$, $y$, $z$ are integer and $x \neq 1$, $y \neq 1$, $x \neq 1$. How do I tell Mathematica to do that?
2
votes
1answer
451 views

FindRoot Infinite expression 1/0 encountered error

I have 1 equation in 1 variable, which when I use Plot, looks like this: ...
3
votes
1answer
337 views

Selecting polynomial roots and plotting against parameters

An implicit function $f(x,k)=0$ is quadratic in $x$ and contains one parameter $k$ which I must vary. Using Solve, I get two real solutions for each specific $k$: ...