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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3 votes
2 answers
198 views

Why is prior manipulation necessary before using 'Solve'?

I wish to use Mathematica to rearrange the following equation: Ia Ra + Ia Ma s == (-Ia + Iref) kp Ma + Ia Ra into this form: ...
0 votes
1 answer
52 views

Plot all real and imaginary roots of FindRoot (2)

Following the comment of our friend @Bob Hanlon's in my post Plot all real and imaginary roots of FindRoot vrs `k`, which I would like to thank again for the assistance it gave, I'm creating a new ...
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0 votes
0 answers
47 views

Solving DE with variable coefficients in Laplace space and inverse transform

Let us consider the following DE: $$y''(x) + f_1(x,s)y'(x) - f_0(x,s)y(x) - g(s)f_0(x,s) = 0,$$ where $x \in \left[-1/2, 1/2 \right]$ and the unknown function $y$ is a function in the Laplace space, ...
5 votes
4 answers
247 views

How do I erase sets of solutions from Solve based on criteria?

I have this list ...
0 votes
1 answer
50 views

How to tell Mathematica to solve an equation assuming all solutions are non-negative reals? [closed]

The title. I have a system of 6 equations that I want to solve. The system is non-linear. I want to solve it, but I just want Mathematica to give me solutions that are non-negative reals (so no ...
2 votes
1 answer
160 views

Plot all real and imaginary roots of FindRoot vrs `k`

I'm looking to plot all real and imaginary roots of this cubic equation eq[x_,k_]:=x^3-5x^2+x-k as a function of a real parameter ...
  • 693
0 votes
0 answers
43 views

Solving implicit function

I'd like to solve for a variable in an expression which is in implicit form. See below. If the u1 and u2 functions below were ...
7 votes
1 answer
120 views

Reshape equation to match pattern

I'm trying to solve some equations and i would like know if it is possible to have the Solve or Eliminate-function arrange the ...
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1 vote
2 answers
123 views

Solving an ODE and a PDE

I am trying to solve coupled sets of (partial) differential equations. For my ODE, I use ...
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2 votes
1 answer
68 views

Solving equation using mathematica

How I can solve the equation : $$R -\tan^{-1}[(m1/m3)*(k3/k1)] - \tan^{-1}[(m1/m2)*(k2/k1)]=0$$ I tried on it using findroot as following : ...
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3 votes
1 answer
64 views

How to improve the following codes for generating eigenvalues?

The following codes generates eigenvalues by using Cebyshev Collocation method of two matrix which consists of another matrices. The codes take more calculation time for larger collocation points, say ...
0 votes
0 answers
33 views

Solving equation with congruences [closed]

I don't have any idea how to write code to solve this problem, any help is appreciated. Thanks in advance.
-1 votes
0 answers
42 views

What's wrong with this solution? [closed]

To solve the elliptic equation, my goal is the universality of this structure. The standard equation form of ellipse is given. In this code, the ellipse crosses the point {2, - 1}, a=2sqrt (2), and ...
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-2 votes
0 answers
28 views

How do I save a Mathematica file as a PDF in our system? [closed]

How do I save a Mathematica file as a PDF?
-5 votes
0 answers
29 views

What are the engineering challenges faced by a software engineering company? [closed]

What are the engineering challenges faced by a software engineering company.
0 votes
1 answer
73 views

Solve for derivative from multiple equations

I'm trying to solve for the derivative of [Psi] with respect to [Theta] from these two equations: ...
2 votes
1 answer
97 views

Shooting technique using NDSolve

Here I am attaching my code below. It took all the variable's values, but the graph window was empty. I am not able to recognize, where is the error exactly. Differential equations were also, checked ...
0 votes
0 answers
66 views

Solve an equation over postive integer [closed]

Solve [x^5 + 2 y^3 == 2684 && x > 0 && y > 0, {x, y}, Integers] I am not able understand this question
0 votes
1 answer
56 views

How to get closed form solution for this cubic equation with parameter [closed]

I am new to Mathematica and I was trying to get closed form equation of this equation by $d$: $$9d^3 - 18d^2 - 12d + 8t = 0, \quad t>1.$$ I tried to get the solution by using $\textbf{Solve}$ as ...
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1 vote
1 answer
83 views

Solving equation with harmonic number and find a parameter [closed]

I need to solve this equation and find k subsequent c. Plz help me🙂 I try to solve it but HarmonicNumber is divergent. So I can’t find solution. In this equation d=0 and r=0.25. I need find k in ...
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0 votes
0 answers
31 views

Solve Inequalities with Functional Arguments

I would like to solve the following inequality: $\frac{(\rho +\tau -1) \left(n g'(n) \left((g(n)-c) F'(g(n))+F(g(n))-1\right)+(c-g(n)) (F(g(n))-1)\right)}{n^2}>0$ Under some assumptions (listed ...
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0 votes
0 answers
32 views

FindRoot::nlnum and InterpolatingFunction::dprec problem

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5 votes
0 answers
291 views

On homotopy continuation method

Consider the following system of nonlinear equations: ...
  • 4,338
1 vote
2 answers
56 views

How to perform item shifting deformation?

How to subtract the two equations. That is, the left subtraction of the two equations is equal to the right subtraction of the equation Continue to the previous question, how to perform the term shift ...
  • 271
4 votes
1 answer
71 views

Studying hyperchaotic finance system

We study the paper "Dynamic analysis and control of a new hyperchaotic finance system" It is given the following system $$X'=Z+(Y-\alpha)X$$ $$Y'=1-\beta Y-X^2$$ $$Z'=-X-\gamma Z$$ with ...
3 votes
0 answers
55 views

Can I use FindInstance to prove an algebraic identity?

This question arose from a [now removed] MathOverflow discussion, where a Null result from a FindInstance query was used to prove that $f(x_1,x_2,\ldots x_n)\neq 0$ has no solution in $\mathbb{R}$. My ...
1 vote
1 answer
51 views

How to compare two ParametriPlots for different problems?

I have solved the following problem for these two situations and created their plots. Now I want to contrast the same axis system in the two plots. I used ...
0 votes
0 answers
48 views

How to solve Equation for different variable in Mathematica?

I want to solve the given equation for $(n=m=3)$ and I want the output variable $q_{1,1}, q_{1,2}, q_{2,1}, q_{2,2}$ Given Equation Given Equation-2 The output should be required Output Here is my ...
0 votes
1 answer
54 views

how to draw the roots of a complex number

I created a simple code to calculate roots of a complex number using De Moivre's formula. I would like to draw these elements. ...
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0 votes
0 answers
41 views

Overflowing during computation in Improved Euler’s method

At my master with have an assignment and we study the Dynamic analysis and control of a new hyperchaotic finance system. For this reason we use Improved Euler's Method with the following code. In ...
2 votes
1 answer
31 views

Create a set of vectors from given pairwise dot product

Assume I am given a list of all the pairwise dot products of an unknown set of $n$ vectors. How can I efficiently generate such a set (or all possible sets) with the extra constraint that all vectors ...
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0 votes
1 answer
53 views

How to convert a fractional equation into an integral equation?

The operation rules are as follows:The coefficients in the equation are not equal to zero,That is to say, in the process of converting to an integral equation, if a common factor is proposed and the ...
  • 271
3 votes
1 answer
115 views

Euler's Method for system of differential equation with more than two functions

According to what I have read, the first formula is the classical Euler method and the second is the improved Euler method for second-order equations. Method A: accuracy of order h ...
0 votes
0 answers
26 views

Error of boundary condition is not specified on a single edge

I am trying to solve a PDE, but Mathematica is showing a strange message which is saying" boundary condition is not specified on a single edge" ...
0 votes
1 answer
39 views

Manipulating boundary conditions of coupled non-linear ODEs using Manipulate and ParametricNDSolve [closed]

I`m trying to plot solutions that are presented for different values of parameter I called "$A$" which appears in the boundary conditions for a system of two coupled nonlinear differential ...
3 votes
1 answer
111 views

How to carry out overall replacement?

There is an equation: (-3 + 4 k^2)/(-6 + m^2) == 1 and a fraction: Sqrt[m^2]/Sqrt[1 + k^2] How can the equation be used to ...
  • 271
0 votes
1 answer
60 views

Not plotting solution to the coupled non linear ODE system using NDSolve [closed]

I`m trying to solve the following system of non-linear coupled first-order ordinary differential equations: $$ \frac{dh}{dx}=-h^2c^2 $$ $$ \frac{dc}{dx}=-hc $$ with the conditions: $$h(5)=5, c(5)=0....
3 votes
2 answers
78 views

Is there an option to automatically make solve return the principal value of inverse trig functions?

I am porting some of my Maple packages to Mathematica. In Maple, solve(sin(y)=x,y) returns arcsin(x) and I'd like to get same ...
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0 votes
0 answers
44 views

Don't run maximize. That I can do

good day. Please, if someone could help me about one problem that I have. How could I maximize the expression and obtained nu and nm? and if possible what would be the expressions of nu and nm if don'...
11 votes
0 answers
119 views

Eliminate variable with partially documented Solve feature Solve[eqns,vars,elims]. Robust?

The Eliminating Variables section on Manipulating Equations and Inequalities documentation quotes an otherwise undocumented feature for Solve ...
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1 vote
1 answer
78 views

The different solution compare to the book solution?

On a book I found an integral with its solution I'm trying to solve it as well in Mathematica 13.2.0 but They are very different?!!!! If anyone can help it out!(integral : Sqrt[(3 x)/(x + 2 d)] d/(x -...
1 vote
1 answer
118 views

Plot in Improved Euler's Method problem [closed]

It is given the following problem: $$x'=rx-bx^2-cxy-\frac{\beta xy}{\alpha+x}$$ $$y'=-\mu y+\frac{\beta xy}{\alpha+x}$$ With parameters $r=1,b=1,c=0.01, \mu=0.4,\alpha= 0.36$ and initial values $x(0)=...
0 votes
3 answers
71 views

How to compare the size of the solution of the equation and assign the value to the corresponding variable?

ClearAll[Evaluate[Context[] <> "*"]] eqns1 = {x^2 - y == 0, y == x + 1}; {{x1, y1}, {x2, y2}} = SolveValues[eqns1, {x, y}] The above equations ...
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2 votes
1 answer
73 views

(Beginner question) How to solve large gradient region from experimental data?

I have a data like this. data ={100, 103, 101, 105, 100, 80, 83, 70, 71, 60, 40, 43, 20, 22, 10, 5, -1, -3, -2, 0, 1, 4, 3, 8, 7, 4, 3, 1, 0, 1, 2, 10, 5, 2} ...
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0 votes
0 answers
65 views

Using Harmonic polylogarithms to solve a partial differential equation

I am trying to solve the following partial differential equation: Eq1:=$f''[x] - ((2*(2*x^2 - 1))/(x*(x^2 - 1)))*f'[x] + 4/(x^2 - 1) f[x] = HPL[{4}, x]/(x*(1 - x)*(1 + x))$ It is told to us that ...
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0 votes
2 answers
164 views

How to compute the rational approximant of a polynomial?

given the chebyshev series expansion up to the fourth order $$f(z)= \sum_{0}^4 c_k T_k(z) $$ with some fixed $c_k$ i need to find the coefficients of the rational approximant (2,1) $$ R_{2,1}= \frac{...
  • 2,549
1 vote
0 answers
86 views

Selecting only one out of many: Differential equation

I have the following code: ...
  • 581
0 votes
0 answers
13 views

Difference Equation with Upper Boundary Condition, Lower Terms Not correct

I am struggling to understand the solution Mathematica is providing for the following recurrence relation As I have written a[i] I expected the following behavior <...
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1 vote
1 answer
67 views

Matrix solving problem

I have a linear system like this: $$\left[\begin{array}{l}x_2\\y_2\end{array}\right] = \left[\begin{array}{l}A_{11}&A_{12}\\A_{21}&A_{22}\end{array}\right]\left[\begin{array}{l}x_1\\y_1\end{...
  • 11
2 votes
1 answer
78 views

Findroot: Boundary value problem

I have an equation, ...
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