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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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
$$\{...
- 3,410
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1
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Plot with solutions of NDSolve
I am trying to substitute the values of phi[z] and phi'[z] back into my equation for Hubb[z] to then plot and compare. The issue I am having is that when I am substituting back into the Hubb[z] ...
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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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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 ...
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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
...
- 8,314
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40
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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
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2
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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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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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Finding Symbolic Expression for x from Derivative of Total Profit Equation
I'm trying to find an expression for x in terms of other parameters from the derivative of my total profit equation. I want to keep everything symbolic, as the equation of x will be used in other ...
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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 ...
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Finding three unknown variables by using Newton-Raphson method [closed]
Why this error happening when finding 3 unknown variables using Newton–Raphson method?
FindRoot[{eq1, eq2, eq3}, {{R, 4003.72}, {\[Beta], 1}, {\[Gamma], 1}}];
...
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1
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Solving system under constraints
I have the system of two equations in the variable $\mu$ with real parameters $A$ and $E$: $$\begin{equation}\label{eq:waveaction_posMu}
\frac{1}{2}A = -\frac{2T}{\sqrt{\frac{\pi^{2}}{3} + 2\mu}}\...
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Poincare section keeps running without giving results
I am trying to find the Poincare section as given in Figure 7 of this paper.
This is the code that I am using for it:
...
- 2,513
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1
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Integer points on a line segment
I have two rational points. They are denoted below in black and they define a line segment. Find integer points on this segment.
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Solving a Coupled System of Partial Differential Equations with Initial and Boundary Conditions
I am working to solve the provided system containing one PDE coupled with an ODE.
$G_t - \frac{\dot H}{H}\eta G_\eta -\frac{1}{H}FG_\eta +\frac{1}{H}F_\eta G + \frac{2FG}{\eta H}=\frac{1}{H^2R}[G_{\...
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Solve an equation perturbatively
I have this equation:
$$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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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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1
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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\...
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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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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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2
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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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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 ...
- 521
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1
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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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1
answer
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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 ...
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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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1
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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 ...
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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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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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1
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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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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 ...
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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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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 ...
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3
answers
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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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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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2
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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 ...
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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 ...
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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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How can I solve a complicated nonlinear equation?
I was tried the following equation using Solve function:
$$h \left(\frac{b m e^{c (r-m)}}{c}-\frac{b \left(m e^{c (r-m)}-r\right)}{c}\right)+k
\left(\frac{b e^{c ...
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1
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How can I know for sure if I have a singularity or not when numerically plotting solutions to ODE's?
Here's my code for what I'm working on:
...
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1
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Solving an integral equation in Mathematica
I have the following equation:
$$ V_I = v_0 - \frac{m G^2}{2 \pi \sqrt{\gamma}}\int_{\infty}^{\infty} \mathrm{d}p \, p \frac{\frac{p^2}{2\sqrt{p^2 + \frac{p^4}{4}}}}{\sqrt{p^2 + \frac{p^4}{4}} + m\...
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Reliability of DSolve to ensure existence of analytic solutions
So I've been wondering about this for a long time. Of course, Mathematica DSolve can be a monster slayer sometimes but as Mathematica as it can get, the output results usually tend to be not ...
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4
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166
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Expansion of implicit function
Related (but not being solved) question: AsymptoticSolve for Taylor Expansion of Implicit Function
I have a implicit function defined as follow
$$
T = \frac{1}{4\pi M}\frac{\sqrt{M^2-(J/M)^2}}{M+\sqrt{...
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1
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1
answer
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FindRoot: Is it a zero or a very small value?
I want to solve the following problem: Given a complex matrix $m=\textbf{m}(J, ω)$, with $J, ω \in \mathbb R$, find $λ$ and $ω$ such that
$$\det[\textbf{m} (J, ω)] = 0$$
I tried to solve it with ...
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"SixJsymbol" function unable to be simplified with long run times due to not real components despite including the assumptions
I'm trying to perform some quantum mechanical calculations using Wigner-Eckhart theorem by running them through Mathematica. However, despite including the assumptions the calculation is unable to be ...
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1
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How to collect the terms with $m_1$ in common, $m_2$ in common and $m_3$ in common in a large expression?
How do I separate the terms in the following expression having $m_1$, $m_2$ and $m_3$? Please help me out. I shall be really grateful.
...
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1
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114
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Assign condition to variable
I would like to integrate the output of a Solve. But Solve gives me an expression with some conditions. I would like to assign this condition to variables.
For example:
...
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2
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91
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How to solve the partial differential equations?
equation is
and the symbol solution is $u[x,y]=e^x \sin(\pi y)$
mathematica code
...
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1
answer
53
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Showing symbolic equality up to some transformation of variables
I'm trying to show that there exists some transformation of variables between the following two expressions such that they are equivalent.
...
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5
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684
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Is there a more concise method to solve the problem of finding tangent lines to curves?
The question is:
If the tangent line to the curve $y=e^x+x$ at point $(0,1)$ is also a tangent line to the curve $y=\ln(x+1)+a$, then $a=$ _______
My method is like this, very cumbersome!
...
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