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Questions tagged [equation-solving]

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

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48 views

Solving a complicated, non-polynomial dispersion relation

I am quite new to Mathematica, so I apologise if the following question is very basic; I can't seem to find an appropriate answer anywhere! I am trying to solve a quite complicated dispersion relation ...
2
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2answers
189 views

How to visualize a Lagrange problem with Mathematica?

I had asked a question here, which I was advised to open a new question for my further problems. I have a function as $f(a_1, a_2) = a_1^2 \sigma_1^2 + a_2^2 \sigma_2^2$, which is subjected to the ...
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1answer
64 views

Is there any possibility to visually examine a Lagrange problem with Mathematica?

I have the function: $f(a_1, a_2) = a_1^2 \sigma_1^2 + a_2^2 \sigma_2^2$, which is subjected to the constraint: $a_1 + a_2 = 1$. I have obtained that: $$a_i = \frac{\sigma_i^{-2}}{\sum_{j = 1}^2 \...
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1answer
75 views

Rewrite a variable in terms of another variable

I have two variables t = 1/Sqrt[2] (Sqrt[1 + Cos[a]] + Sqrt[1 - Cos[a]] + Sqrt[1 + Cos[b]] + Sqrt[1 - Cos[b]] + Sqrt[1 + Cos[c]] + Sqrt[1 - Cos[c]]) and <...
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0answers
64 views

Axes ticks scaled in powers of ten

I'm trying to plot the solution of an ODE and I would like to have the ticks in powers of ten. Although, this happes automatically from Mathematica for small orders, such as ...
6
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2answers
659 views

Why does Mathematica not give the simple solution of the given equations?

I want to solve this system of two equations for $x$ $$\{ \sin (2\pi x)+\sin (\frac{2\pi}y)=0 \quad , \quad \cos (2\pi x)-\cos (\frac{2\pi}y)=0 \} \qquad (1)$$ I use ...
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0answers
52 views

NArgMax returns not a number error

I have the following code: ...
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0answers
46 views

Solve set of equations for function [closed]

I have a set of two equations linear in two functions a[r,t] and b[r,t]. However, in these equations other functions like ...
2
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2answers
174 views

How can I make sure that there are real roots for the given function? Can I trust the plot only?

I have this function $$f(x)=(\pi -2 x)^2 \sin \left(\frac{\pi ^2}{2 x-2 \pi }+\frac{1}{2} \csc ^{-1}\left(\frac{4 \pi (\pi -x) \csc \left(\frac{\pi ^2}{x-\pi }\right)}{4 (\pi -x)^2+\pi ^2}\right)\...
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1answer
140 views

Why this equation cannot be solved in Mathematica?

I do not understand why the following equation cannot be solved in Mathematica. Solve[Log[(-Exp[x] + Sqrt[2 - 3*Exp[2*x]])/2] == c*x, x] The left hand side is ...
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0answers
43 views

Defining parametric function resulting from DSolve

I am trying to define a function that is a solution of a simple ODE with a parameter, for example ...
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1answer
50 views

Understanding plot of Root[] object

I'm trying to understand the plot of this Root object ...
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0answers
47 views

I want to solve 6 equations with three variables. How to solve it? [closed]

I have a 3 \times 3 symmetric matrix equation with 3 variables. Thus, I get 6 different equations of three variables. There is one more variable which can be varied in a given range. How can I solve ...
2
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0answers
41 views

Superfluous un-simplifiable condition returned by Reduce

No real "problem" here, just wondering why this is happening and how one might force Mathematica to simplify this. Consider: ...
7
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1answer
208 views

Steffensen's Method Implementation in Mathematica

This is sort of a math and Mathematica Language question since I do not know which one is going wrong. I am trying to implement Steffensen's Method for Nonlinear Systems of Equations and the first ...
6
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3answers
472 views

Prove an inequality over the reals, given a constraint

Given $a,b,c \geq 0$ and $$a + b + c = 3$$ prove $$\frac{a}{b^2 + 1} + \frac{b}{c^2 + 1} + \frac{c}{a^2 + 1} \geq \frac{3}{2}$$ One can prove the above using a great deal of "human" insight ...
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1answer
131 views

There are some warnings thrown with NDSolve here. How can I change my code to avoid them?

I want to solve some differential equations, but the warnings "NDSolve change the value" are thrown. How do I change the equations? Are there some equations that are not allowed? Are some ...
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1answer
131 views

NDsolve to solve Nonlinear Schrödinger or Gross–Pitaevskii Equation?

I am trying to used NDsolve to solve Nonlinear Schroedinger Equation: ...
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1answer
53 views

How to use Nsolve to tackle a Bessel-related function?

I tried to get the result of the value of ncoeff as the function of wl,codes was pasted blow as well as the picture in MMA,can somebody give me some guidance ,cause my codes take a long time though,it ...
5
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1answer
76 views

DSolve inconsistently able to evaluate expression

I am trying to use DSolve to evaluate a coupled system of ODEs as follows DSolve[{Y0[X] + Y0''[X] == 0, Y1[X] + Y1''[X] == X Y0[X]}, {Y0[X], Y1[X]}, X] However, ...
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2answers
48 views

Using NSolve to get a solution for Bessel-related functions

I want to get a solution of a equation using NSolve. $BesselI[1,x]/(x*BesselI[0,x])=0.2$ So I plugged this equation to NSolve: ...
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1answer
112 views

Is the following equation solvable by Mathematica? [closed]

I want to solve and plot the solutions of the following equation, where Mathematica is still running and doesn't return anything: ...
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1answer
42 views

Plot the region given by inequaities

How can one visualize the regions of intersection of the following ...
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0answers
52 views

FindInstance: How does it work for linear inequalities?

I have a set of linear inequalities, rational coefficients. When FindInstance returns {}, does that really mean there is no ...
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0answers
53 views

solving ordinary coupled differential equation

I have a set of 8 ordinary differential equations containing matrices which I need to solve using initial conditions. I have written the equations in this form: ...
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0answers
69 views

time evolution in time dependent hamiltonian

I have a time dependent Hamiltonian(A(t)) which NOT commutes at different times. dU(t)/dt=A(t)U(t)+n(t) How can I find the time evolution operator of this system so that I can solve it in Mathematica? ...
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1answer
62 views

Construct a matrix from its elements and solve the eigenvalue problem

I want to construct a 10 by 10 matrix whose elements are given by $$ H_{nm}=\delta_{nm}\left (n^2+v[b_1-b_0-h(2m,b_0,b_1)]\right) \\ +v(1-\delta_{nm})\left (h(n-m,b_0,b_1)-h(n+m,b_0,b_1)\right) $$ ...
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1answer
52 views

Stationary Distribution of Markov Chain [closed]

I'm trying to compute the stationary distribution of the following Markov chain: $$P=\left( \begin{array}{cc} p_{11} & p_{12} \\ p_{21} & p_{22} \\ \end{array} \right)$$ I know you have to ...
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0answers
38 views

Equation issue: Solve gives an empty output

I need c1,c2....c9 values. Why is Solve returning an empty list? How i can fix it? Thanks for any advice. ...
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1answer
65 views

Plotting equation with some unknown parameters

I am new to the Mathematica and I have a question about the plotting. I am trying to plot the transcendental equation $$\tan{(z)}=\sqrt{\frac{1}{2m_0}\left (\frac{z_0}{z}\right)^2-1} $$ where the ...
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0answers
89 views

Creating An Input That Crushes The Application and/or Computer?

Dear StackExchange Users, Can anyone assist me in creating a line of input that will malfunction the Wolfram Mathematica 12.3 application (and ideally the computer) when it executes/been executed? In ...
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1answer
77 views

No solution to the equation even though it has one

I was trying out Mathematica with a simple equation. I tried this one out, but it outputted nothing and when I went on WolframAlpha to test it, there was a result (c = 3 btw). Please let me know if ...
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1answer
62 views

How to find the integer numbers a, b, c, d, e, m satifying the following conditions?

I know that, the function f[x_] := (x^2 + 6 x + 5)/(x^2 + 2 x + 3) with D[f[x], x] have two integer solutions ...
3
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2answers
170 views

Aren't roots of polynomial equations smooth functions of their parameters?

I am trying to find the solution of cubic equation as a function of $kz$ ...
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0answers
65 views

Plot is fast, solve is slow - what optimizations can be made?

I'm trying to solve a 3D geometric problem in terms of 3 variables (rotational angles), and I think the end is finally in sight - quite literally, I can see on a 3D plot where my solution exists. ...
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1answer
31 views

finding min S such that integral is greater than some value

I have this function $R(r)$, and $r*R^2$ is a probability density function. ...
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1answer
62 views

Trouble while trying to re-run open source code

I am a physics student and this is my first time working with Mathematica. I am trying to run the notebook mentioned here, titled "Amplification factors of the superradiant scattering of a ...
1
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1answer
64 views

Speed up FindRoot

I need to calculate Sv[zm,zs,zh] for a given range of zm and zs with fixed ...
1
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1answer
54 views

how we can extract the value of the solution of a PDE in a point x? (NDSolve) [closed]

Please I need your help, I calculate the solution of heat equation using methode of line This is my code: ...
15
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2answers
650 views

Nice cubic polynomials

Let a polynomial with integer coefficients be nice if this polynomial has distinct integer roots; its derivative has also integer roots. For instance $$p(x)=x(x-9)(x-24),\\ p'(x)=3(x-4)(x-18)$$ is ...
0
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1answer
50 views

How to solve differential equation with integrating factor method? [closed]

I need to solve first order differential equation of this type: $$\dfrac{\partial T_1}{\partial T_0} + a \dfrac{T_1}{T_0} = f (T_0)$$ I know it need to be integrating factor method, but I don`t know ...
1
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1answer
45 views

Reducing a sum of two cube roots

I'm trying to verify that this sum of cube roots is equal to 1, using Solve, ToRoots, ...
0
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1answer
62 views

Why one root is missing for this equation?

I solved this symbolic equation and it has 3 roots. ...
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1answer
83 views

NDSolve of a stiff system of ODE's

I am trying to solve numerically the following set of differential equations ...
0
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1answer
27 views

How to resolve problem during summation of functions?

I am trying to find out the output of this basic problem but getting an error. If anyone can resolve this will be helpful. ...
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1answer
88 views

How to solve this system of equations [closed]

How to solve the following system of equations (If it is possible, I am seeking exact solutions) ...
0
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1answer
89 views

Modification of Variable In Parametric Plot 3D

I am plotting a 3D plot of my set of ODEs. The ODEs are as follows: ...
4
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3answers
172 views

Simplifying the output to Reduce

I am trying to solve a system of inequalities in Mathematica using Reduce: ...

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