Questions tagged [equation-solving]
Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
6,658
questions
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While solving equations I'm getting error [closed]
These pictures give you the governing differential equation to solve with boundary conditions. While I'm solving the equations I'm getting an error.
1
vote
0
answers
20
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Unexpected Peaks and Detours in PNJL Model Plot Using FindRoot
I'm working on a numerical solution for a PNJL model. The model I’m working on is based on the formalism described in this paper: arXiv:hep-ph/0506234. My goal is to reproduce plots similar to the ...
0
votes
0
answers
67
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How can I solve this large system of linear equations?
I have a large system of linear equations of the form:
$$
\begin{equation}
\begin{split}
\alpha_{11} c_1 + \ldots + \alpha_{1n} c_n &= 0\,, \\
\alpha_{21} c_1 + \ldots + \alpha_{2n} c_n &= 0\,,...
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43
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Solve is not not working when I am using s as variable instead of x?
The following is the code.
...
- 1,715
0
votes
1
answer
82
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How am I able to find poles in this equation?
this following is my code for KVL, KCL in circuit analysis.
I want to calculate $\frac{V_{D1}} {V_{in}}$ and $\frac{V_{s}} {V_{in}}$
...
- 1,715
2
votes
2
answers
170
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Find conditions for a cubic to have three positive roots without explicitly using the Root objects?
According to this question, the solutions to the equation $x^3 + p x^2 + q x + r = 0$ ($p, q, r \in \mathbb R$) are positive iff $p < 0$, $q > 0$, $r < 0$, and $-27 r^2 - 2 p {\left(2 p^2-9 q\...
- 537
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votes
3
answers
173
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Question on the root [closed]
Is it true that the smallest root $t$ of the polynomial
$$
20 t^3 - 30 t^2 + (12 - 4 \cos^2 \alpha - 4 \cos^2 \beta - 4 \cos^2 \gamma) t + \cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma - 2 \cos \alpha \...
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61
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-1
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0
answers
51
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Numerical Solution to Euler Lagrange Equation [closed]
I am quite new to wolfram. would anyone share how to solve the euler lagrange equation (equation at the bottom), by using variables from equations above. thank you
0
votes
3
answers
127
views
How to find conditions such that solution to linear system of equations exists?
Say I have some complicated equation that contains some constant variables like this
...
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4
votes
0
answers
75
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Solving a matrix differential equation with change of variable
In order to solve $\partial_t X(t) = -i(M X(t) - X(t) M^*)$ (where * is conjugate-transpose), I wrote the following code:
...
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3
votes
1
answer
102
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Finding Jacobian from Hamiltonian
Suppose I am given a Hamiltonian. How do I find the Jacobian from the Hamilton equations of motion? Here is what I have done so far:
...
- 2,553
7
votes
3
answers
689
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NSolve uses all CPU resources
Is it default setting of NSolve that it uses all my four cores of CPU?
Be aware that the following code made my computer non-respondent for about 18 seconds till it ...
- 21.4k
0
votes
0
answers
54
views
Finding Lyapunov exponents from Hamilton formalism [closed]
I have the following Mathematica code to find the Lyapunov exponents for a given Hamiltonian. I use an algorithm developed by ChrisK for my code given below:
...
- 2,553
2
votes
0
answers
60
views
Need help to find a generalized solution for a given system
I'm solving two sets of equations, the equations are given below,
$-\frac{t'[\lambda]}{z[\lambda]^{2}}+\frac{z'[\lambda]^2}{z[\lambda]^2}=1$
$t'[\lambda]^2=\frac{p^2 z[\lambda]^{2}z'[\lambda]^2}{1+p^2 ...
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1
vote
0
answers
63
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Why is the solution to a harmonic equation split into two classes when one class suffices?
If we solve $\sin(x) = 0$, we arrive at $$x = n \pi, n \in \mathbb{Z}$$
When I do (Reduce also returns the same)
Solve[Sin[x] == 0, {x}, Reals]
The result is
$$\{...
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1
vote
1
answer
60
views
-2
votes
1
answer
71
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Why is it that defining the range of angles makes it impossible to find a solution Sin[a + b]==-((2 Sqrt[2])/3)?
Given that α is an angle in the first quadrant and β is an angle in the third quadrant, and tan α + tan β = 4, tan α tan β = √2 + 1, then sin(α + β) = __________.
Without limiting the range of angles ...
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0
votes
1
answer
22
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Parallel solution of several functions [duplicate]
I have a large and complex function with 5 variables f[a_, b_, c_, d_, e_] and three specific values for e, say e1, e2, e3. I substitute these values in f and treat them as three new functions, like ...
4
votes
2
answers
173
views
Solve cannot find solutions if integer parameters are assumed
This is a very simple toy problem that illustrates the problem.
Start with a fresh kernel.
Quit[]
Make some simple assumptions
...
- 8,334
0
votes
0
answers
42
views
Encountered non-numerical value for a derivative at t == 0 with NDSolve
I am trying to use NDSolve to compute the solutions for a master equation of a 6x6 density matrix, equivalent to 21 first order coupled ODEs.
The equations are computed as follows
...
1
vote
2
answers
74
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How to solve a matrix equation involving Rank
Given that the matrix $A = \begin{bmatrix} 0 & 1 & 1 & 1 \\ 1 & 2 & 1 & 2 \end{bmatrix}$.
I want to solve for the matrix $B= \begin{bmatrix} a & 0 & 0 & 0 \\ 0 &...
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3
votes
1
answer
196
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How to symbolically solve a coupled system of equations with Mathematica?
The symbolic solvers of Mathematica are strong, however, the ones fail
in some cases, for example, for the system {x^(x + y) == y^12, y^(x + y) == x^3} over the ...
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1
vote
1
answer
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Is it possible to make an ODE-based system component that can be used repeatedly?
The background to my probelm:
The problem I want to address is the seismic response of a bridge after installing dampers. The kc component here refers to the ...
- 1,467
1
vote
1
answer
87
views
Solving system under constraints
I have the system of two equations in the variable $\mu$ with real parameters $A$ and $E$: $$\begin{equation}\label{eq:waveaction_posMu}
\frac{1}{2}A = -\frac{2T}{\sqrt{\frac{\pi^{2}}{3} + 2\mu}}\...
- 521
2
votes
1
answer
116
views
Poincare section keeps running without giving results
I am trying to find the Poincare section as given in Figure 7 of this paper.
This is the code that I am using for it:
...
- 2,553
0
votes
1
answer
61
views
Integer points on a line segment
I have two rational points. They are denoted below in black and they define a line segment. Find integer points on this segment.
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2
votes
1
answer
85
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Solving a Coupled System of Partial Differential Equations with Initial and Boundary Conditions
I am working to solve the provided system containing one PDE coupled with an ODE.
$G_t - \frac{\dot H}{H}\eta G_\eta -\frac{1}{H}FG_\eta +\frac{1}{H}F_\eta G + \frac{2FG}{\eta H}=\frac{1}{H^2R}[G_{\...
4
votes
1
answer
374
views
Solve an equation perturbatively
I have this equation:
$$T=2 P r-\frac{q^2}{4 \pi r^3}+\frac{1}{4 \pi r},$$
and I want to solve it for $r$ perturbatively. This result should be: $$r=\frac{T}{2 P}-\frac{1}{4 \pi T}+\frac{P \left(8 \...
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2
votes
1
answer
60
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How to solve a polynomial made up of vector components for t
So I am trying to symbolically solve a polynomial equation in mathematica that is described with vectors:
...
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votes
1
answer
105
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Solving system of two equations
For $\mu \in (-\infty,-\frac{\pi^{2}}{6})$, I need to solve for $T$ and $\mu$ the system
$$ \frac{1}{2}A =\frac{2T}{\sqrt{-(\frac{\pi^{2}}{3} + 2\mu)}}\arctan{\frac{\pi}{\sqrt{-(\frac{\pi^{2}}{3} + 2\...
- 521
1
vote
1
answer
112
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Getting conditions for existence of trigonometric solutions
Consider the following problem. Define a trigonometric function f(x):
f[x_]:=a*Sin[2*x]+b*Cos[2*x]+c*Cos[x]+d*Sin[x]-e
We want a range of $x$ for which $f(x)\leq 0$...
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1
vote
1
answer
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Solution Of 2D Logarithmic PDE In Periodic Potential In Imaginary-Time Propagation Method
I am trying to solve Eq.no.(8) from https://arxiv.org/pdf/2009.06804 and generate Fig. (3)-(4). The problem I am facing is that in imaginary time propagation method the solution is growing with time ...
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0
votes
2
answers
186
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How to use Lagrange multipliers to find the maximum value with constraints?
How can the Lagrange multipliers method be employed to optimize the function?$f(x_1,x_2)=(x_1^p+x_1^p)^{1/p}$
subject to the constraint $g(x_1,x_2)=p_1x_1+p_2 x_2-y=0$
I am a beginner, and the results ...
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1
vote
1
answer
95
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Solving a system of two equations for only real solutions
I have a system of two equations
\begin{align}
\frac{1}{2}A &= \frac{2.5 T}{\sqrt{-(\frac{\pi^{2}}{3} + 2\mu)}}, \\
\frac{1}{2}E &= \pi T + \frac{\mu}{2}A
\end{align}
in which $A$ and $E$ are ...
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votes
1
answer
71
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Any other better way to draw a dynamic tangent to a curve? [duplicate]
I want to draw a dynamic diagram of the tangent line at any point on the curve y = =Log[x].
...
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3
votes
1
answer
172
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Duffing Equation:Transition to Chaos
I create the following code but the results were not that I expected for. The paper I study is Duffing Equation
My code gives me the following. But I want a smoother and clearer plot. What should I ...
0
votes
0
answers
32
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Solving expression with incomplete gamma function and plotting
In the following code I want to plot fplot1 vs P by substituting r from ...
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0
votes
1
answer
51
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How do I invert this function?
I have the following function that I want to invert to use in further calculations, i.e. I need to be able to plug in the expression $r = r(p)$ in further calculations where $r$ goes over the range ...
- 131
3
votes
3
answers
900
views
Why are these simple equations so slow to `Solve`?
$Version
(*14.1.0 for Mac OS X ARM (64-bit) (July 16, 2024)*)
This set of equations is generated by other codes and hence is redundant:
...
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votes
1
answer
124
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I have a error on my code but I can't find it!
I have a problem by my code I can't find it yet!!
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vote
1
answer
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How to check equivalence when variables in equations are replaced by their negatives?
In a previous post about checking whether two systems of equations are equivalent, the suggestion was to use the Reduced Row Echelon Form, which was great.
However, I now want to consider an ...
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votes
1
answer
110
views
Simplifying an ODE in Bessel notation
I have the following Mathematica code:
eq[r_] = 3 (1 + 2 a) g1 r y[r] - 2 (2 y'[r] + r y''[r]);
DSolveValue[eq[r] == 0, y[r], r]
This gives me the ...
- 2,553
0
votes
2
answers
91
views
Plotting a set of equations [closed]
I have two following eqs:
$S = a M^2 + \beta + \alpha Log[a M^2]$
$t =\lambda^5 M^5 (3 + \lambda^2 M^2)/
3\delta (1+\lambda^2 M^2)^2$
where a, $\alpha$, $\beta$, $\delta$ and are constant parameters. ...
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0
votes
1
answer
80
views
FullSimplify returns complex number even though assumptions make it real
EDIT: Maybe the scope of my question is really how to solve in closed-form for the real roots of the cubic, conditional on being in the parameter space where the discriminant is positive.
So I'm ...
2
votes
3
answers
157
views
How to check if two homogeneous systems of linear equations are equivalent?
How can I check if two homogeneous systems of linear equations are equivalent in Mathematica?
Given two systems of equations:
System 1:
\begin{cases}
2x - 3y + 4z = 0 \\
-5x + 6y - 7z = 0
\end{cases}
...
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0
votes
0
answers
73
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Equation solving and variable manipulating issue
Another difficulty I am facing in Mathematica. I have an equation with r and P as variable. when I put value of P and then solve for r, I am getting a solution. but if I try to solve for r first and ...
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0
votes
2
answers
96
views
Plot an expression in which a variable satisfies an equation
My question is very simple. I have a function $f(r)$ with some other parameters and I want to plot ${f'(r)}/{4\pi}$ vs P where r is satisfying the equation $f(r)=0$. I don't know where am I doing ...
- 119
0
votes
1
answer
99
views
Estimation of particle displacement in meters from consecutive images
I have two images (img1,img2) in which the particles have moved. I obtained their displacements from the ImageDisplacements command, but I don't know how to ...
- 155
0
votes
0
answers
25
views
FindRoot[NDSolve...] [duplicate]
I have a function OdvodNaPolu: $\mathbb{R}\to\mathbb{R}$, and I want to find its zero. The function contains NDSolve and based ...
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