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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64 views

Finding fixed points of a system of difference equations

Can anyone help me in finding the fixed points of the systems satisfying all the parameters are real, positive? $$x_{n+1}=x_{n-d}e^{(r(1-\frac{x_{n-d}}{k})-\frac{\beta y_{n-d}}{(x_{n-d}+\gamma)}+x_{n-...
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2answers
81 views

How to solve this inequality? [closed]

solve for the smallest N value for this inequality, I tried several online calculators and they are not working.
4
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1answer
127 views

Solve efficiently large system of $N$ quadratic equations

I am trying to find all $\lambda$ given a tensor $T$ such that $\sum_{jk}^N T_{ijk}x_jx_k=\lambda x_i$ with $1\leq i \leq N$ and $\sum_i x_i^2=1$. $T$ is known but $x$ is unknown. This boils down to ...
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1answer
54 views

Solve four equations system considering that the picked solution should minimize a function

I wrote equations that represents the rotation on a gimbal system for pointing a telescope with 3 DOF, I have a system in four equations and 4 unknowns, but as you can figure out easly the system has ...
3
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2answers
103 views

Are all the solutions produced? [closed]

Here is a very strong and impressive result of the Reduce command. Reduce[a^2 + b^2 == 841*(a*b + 1), {a, b}, PositiveIntegers] ...
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1answer
53 views

Using ContourPlot3D to fine the local extrema of a 3D function

This answer shows a neat way of using ContourPlot and MeshFunctions to find the local extrema of a 2D function: the ...
3
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1answer
104 views

Solve system of trigonometric polynomials

I am trying to solve a real system of trigonometric polynomials, which contain 7 symbols {b[1],b[2],b[3],b[4],a[2],a[3],a[4]} between 7 equations: ...
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1answer
62 views

Solving ODE for emptying water tank, exclude branch with complex infinity

I'm trying to simulate a water tank. The dynamic of the system should be described by: DSolve[{y'[x] == Piecewise[{{-Sqrt[y[x]], 0 < y[x]}}, 0.], y[0] == 10}, y[x], x] An infinite object ...
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1answer
88 views

Newton's Method plot [closed]

I'm trying to do c. So far I tried, ...
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0answers
49 views

Reduce : This system cannot be solved with the methods available to Reduce

I have a few expressions and need to get a final simplified (reduced,solved) results. I am new and tried/searched different ways for my problem but couldn't find the reason. These are my expressions: <...
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1answer
46 views

How can I substitute values into this set of equations?

I'm new to Mathematica and I'm trying to solve this set of trig equations (I'm not exactly sure if the syntax looks correct): ...
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1answer
56 views

Solving a complicated time-dependent function

I want to solve the following time-dependent system of equations: ...
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0answers
35 views

NArgMax solutions' intersection plotted but not solved for

Defining two functions via NArgMax and plotting, there is an intersection and the Plot function works. But trying to solve for ...
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1answer
109 views

NSolve and NIntegrate, or a better approach

I need to define and plot the following function $$ a(t) := \exp\left(\int Z(t)\; dt\right) $$ where $Z(t)$ is the solution to the equation $$ 0 = t - 2 \int^Z_1 F(x)\; dx $$ with $F = F(x)$ being a ...
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1answer
85 views

Can I use Solve to solve for an expression (instead of a variable)?

I have an equation:$$ds^2=-(C_1+A\space t)^2 dt^2+C_2^2 dr^2$$How would I re-arrange this formula to get an expression of $\frac{dr}{dt}$? $C_1$, $C_2$ and $A$ are constants. I know the answer is:$$\...
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2answers
86 views

Command to know when it become constant

So I got this equations and I want to know if there is a command to know when the function becomes constant and obtain that value, this is my code and I know that approximately at 2600 both functions ...
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1answer
62 views

Reduce the time to find six integer numbers so that the angle of two vectors equal to Pi/6

I am trying to find six integer numbers a, b, c, x, y, z so that the angle of two vector {a, b, c and ...
5
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1answer
101 views

How is Mathematica treating $x^x$ when finding roots?

When I enter Solve[x (-x + x^x) == 0, {x}, Reals] It returns three roots as $$\{\{x\to -1\},\{x\to 1\},\{x\to 1\}\}$$ Is MMA treating ...
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1answer
38 views

NSolve hangs on what should be a simple problem

This hangs: ...
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0answers
24 views

Why doesn't work the maximize and reduce?

Alguien puede ayudarme por favor? He estado tratando de resolver y hallar en base a las funciones maximizar y reducir, la expresion de P y sus restricciones, pero no he podido obtener. ...
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1answer
47 views

How can I use “Reduce” to solve equation with complicated form?

Here I used Reduce to solve that complicated equation in complexes but MMA didn't give an answer after a few mins. I wonder whether there're some functions could ...
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0answers
31 views

Rescale root of quartic equation

I have a quartic equation $1-r+\frac{1}{w^2}r^4=0$ where I am interested in the plot of $\frac{1}{w} f(r_0)$ (equal to $f(r_0/w)$) where $r_0$ is one of the roots. I would like to rescale the roots ...
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0answers
30 views

Assume some expression is false

I need to Reduce a complicated function and I want to exclude some conditions A and B. How do I assume that the expression A is ...
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1answer
62 views

How to get the intersection between circle and rectangle?

Consider two figures: a rectangle with coordinates $(x_{min},y_{min}), (x_{min}+dx,y_{min}+dy)$, and a circle. The latter has a radius $R$ and is located at the center of the coordinate frame. How to ...
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2answers
98 views

Solving a non-linear system of equations symbolically [closed]

How would I solve this systems of non-linear equations symbolically: $$ \mu N -\frac{\beta S I}{N} - \nu S = 0 \qquad (1)$$ $$\frac{\beta S I}{N} -\gamma I - \nu I = 0 \qquad (2)$$ $$\gamma I - \nu R =...
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1answer
51 views

Plotting a parametric system of two differential equations

I am trying to solve the system of parametric equations below. The initial value ranges, in order to find the critical point where N[s]=0 and D[s]=0. What is the best way to do this? How can i plot ...
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2answers
45 views

Solving a hyperbolic equation

I have the following equation: Tanh[-19.4*\[Zeta]]*Exp[k x] == Tanh[-19.4*\[Psi]]; \[Zeta] = 66; k x = 9.21; I want to calculate the value of ...
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1answer
33 views

Why not getting the plot using NSolve? [closed]

I am trying to plot using these equations in NSolve but not getting any graph. I don't know why it is happening. Usually, these types of equations solved easily but I don't know where I am doing the ...
2
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1answer
82 views

Solve[] arbitrarily adding orders of magnitude which cancel?

Define the variables m0 = .1349766; mp = .13957018; mX = (2 mp + 3 m0)/2; Now suppose we wish to solve the following equation for equation ...
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0answers
26 views

PDE solution positivity constraint [duplicate]

I have a 2d PDE and NDSolve returns a solution that takes negative values but I want the function to be positive f[x,y]>=0 everywhere. How do I include ...
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2answers
72 views

How can I solve this equation involving an infinite sum of Harmonic number powers?

V[x_] := Exp[x^2] - 1 T[x_, b_] := Sum[Exp[-b*x^2*HarmonicNumber[i]], {i, 1, Infinity}] Solve[T[x, b] - V[x] == 0, x]
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0answers
45 views

Piecewise PDE Over 3 Regions with Continuity Boundary Conditions

I am using Wolfram Language for the first time for my research and could really use some help! I am trying to find the analytical solution of a PDE which has piecewise constants and a piecewise input. ...
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1answer
30 views

Condition of existence while solving inequalities

I would like to have solutions of inequalities where condition of existence are included, but Reduce doesn't work like this, it would simplify the denominators ...
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1answer
46 views

How can I solve a linear equation with many input variables symbolically without taking forever

Background: I have a linear equation whereas T2 and T3 are transformation matrices, Rp is ...
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0answers
76 views

How to do deconvolution

I have these 3 equations: Now I want to calculate the function f(x). The f(x) should like this: Here a1-a7 are constant parameters. Could someone tell me how to calculate the f(x)? Thank you very ...
2
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0answers
33 views

How to change the size of the y axis

I got this code but the solution is very tight in the Y axis, I wanna know how can I change the scale or the size of the Y axis and how can I obtain its solution cause it's not as simple as ...
3
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0answers
29 views

Numerically solve a non-differential equation with InterpolatingFunction as output

I have some a function that I need to solve numerically over an entire domain (Ideally I would like an InterpolatingFunction object as output), which does not include any derivatives. I have found a ...
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1answer
46 views

How to make FindRoot work with PolyLog functions

I have the following code: ...
2
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2answers
130 views

Minimization using NMinimize

I have a system of ODEs say $$x'(t)=2 x(t)-x(t)y(t)-3 x(t) g(t),$$ $$y'(t)= y(t)-2 x(t)y(t)- x(t) g(t)$$ with ICs $x(0)= 1, y(0)=1/2$, say, for $t_0 \leqslant t \leqslant t_f$, where $t_0$ and $t_f$ ...
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1answer
87 views

Can NDSolve be used for a system with number (+40) of equations?

I have 42 coupled differential equations (6 of them are PDE's). My system has 6 objects and an object have 7 coupled equations. Since these objects are interacting with each other, their coupled ...
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0answers
16 views

How to force N[ ] to output the real value (or all values) for negative cube roots [duplicate]

Evaluating N[(-1)^(1/3)] returns 0.5 + 0.866i in my v12.0 notebook. Of course, the equation x^3 = -1 has three distinct solutions for x. Is there a global (or local) option that will force Mathematica ...
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1answer
26 views

Is there a better way : solutions to integer equation

I have the following code which solves for Integers the equation $$a_1+a_2+a_3+a_4+b_1+b_2+b_3+b_4+c_1+c_2+c_3+c_4=tot$$ with $$ -4<a_i\in \mathbb{Z}<4$$ $$ -7<b_i\in \mathbb{Z}<7$$ $$ -4&...
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2answers
71 views

Solving a recursive equation iteratively (including PolyLog function)

I have the following equation which I want to solve: $$ I_D = [Li_2(-e^{V_D-I_D})-Li_{2}(e^{I_D})] $$ Here $Li_2(x)$ is the PolyLog function of order $2$. Is there a way to solve this equation ...
1
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1answer
55 views

Finding the joint domain for a couple of functions of three variables

I have two functions $f_{1}(x,y,z)$ and $f_{2}(x,y,z)$ defined respectively as ...
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1answer
23 views

Manipulate parametters inside NSolve with complex variable

I think my question should be simple but I couldn't figure out a nice way to do it. I want to find zeros of a complex function (variable $z$) with real parameters ($\nu$, $\alpha$, $\xi$). My goal is ...
0
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1answer
59 views

FindRoot not obtaining solution for nonlinear system of log equations

There is a system of 9 non-linear equations, eq containing logarithms that I think it should be solvable numerically. There are a total of 9 variables with two of ...
0
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1answer
46 views

How to refer a solve answer to NDsolve [closed]

I don't know how to refer a solution of Solve to compute it in NDSolve, here's my code ...
1
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1answer
30 views

Read the graphic at another value

So I got this code and I'm new at coding, what I want to do is just read the graphic at a value of the Y axis and get the value of the X axis ...
2
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2answers
59 views

Obtaining the other axis value

I'm new at coding and I got this simple differential equiation and the plot of this function involved, I can obtain the value of the dependant variable based on the independant varible as usual, what ...
4
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1answer
231 views

How to solve vector equation?

Given the vector relation $(\mathbf{a}+3 \mathbf{b}) \perp(7 \mathbf{a}-5 \mathbf{b})$, $(\mathbf{a}-4 \mathbf{b}) \perp(7 \mathbf{a}-2 \mathbf{b})$, find the angle between $\mathbf{a}$ and $\mathbf{b}...