Questions tagged [equation-solving]
Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
6,863 questions
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Solving a coupled 2nd order differential equation numerically using NDSolve
I would like to solve the following system of differential equations numerically for two one-dimensional functions $R(x)$ and $\phi(x)$:
\begin{eqnarray}
c_1 \left(R''(x) - (\phi'(x))^2 R(x) \right) - ...
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The heat conduction equation of solar cells can't be solved [duplicate]
The heat conduction equation of solar cells can't be solved. NDSolveValue::ndnum: Encountered non-numerical value for a derivative at x == 0. ...
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Mathematica does not give me any contour here
I would like to have an idea what kind of curbe is being formed from the intersection of the plane $x+y+z=9$ with the surface
$\sqrt{16-x^2}+\sqrt{25-y^2}+\sqrt{36-z^2}=12$ under the restriction $x,y,...
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How to find x ranges where a function is one-to-one and its output is in a given range?
I have a list of functions like this:
...
- 1,417
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The general solution from Solve does not simplify to the specific case
I am trying to get a solution of equation with many parameters. The general solution does not seem to reduce to a specific one.
The specific solution with all parameters known is
...
- 5,650
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How should we formulate angle geometry constraints in Mathematica to help the solving system work more efficiently and speed up the solution process?
Quadrilateral $ABCE$ is a parallelogram. Point $D$ lies on segment $AE$. The diagonals of quadrilateral $ABCD$ intersect at point P. If $△ABP∼△CBD$ and $AB<BC$, find the ratio $\frac{AB}{BC}$.
The ...
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Are there any good ways to improve this code so that it can solve the geometry problem？
While using Mathematica to solve the following geometry problem, my computation has been running for a long time without producing any result.
The geometry problem is:
Quadrilateral $ABCE$ is a ...
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How can I add inequality constraints to Solve? [closed]
How can I add constraints to the Solve function?
For example, I tried:
...
- 1,417
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Parameter search problem for satisfying an inequality
I am working with a $2 \times 2$ matrix
...
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Using symbolic expression in Compile
I found a Mathematica notebook on the internet, which calculates the inverse kinematics of a 6DoF robot.
link to the notebook
In one part of the code it gives a symbolic expression using the Solve[] ...
- 11
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Symbolically solving a set of three-variable nonlinear equations fails to get a simplified result
I want to use Solve to find symbolic solutions of the following set of equations and get simplified or factorised symbolic solutions. The equations are
...
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How to make DSolve obtain this solution to this IVP first order ODE?
V 14.3 can not solve this IVP(Initial value problem) first order ode from textbook
...
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Using the Solve function appropriately
I will discuss the background of this problem first. I have an automated code, which solves linear equations recursively. The number of equations could be of the order of thousands. And, more ...
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Why is the Backsubstitution not working in Reduce in this case?
In the following system why is the Backsubstitution not working:
...
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Why doesn't InverseFunction give a continuous function?
I would like to get a smooth solution using InverseFunction. However, the code doesn't work as I expected.
...
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AsymptoticSolve returns the input
I have the following input
Assuming[\[Epsilon] != 0,
AsymptoticSolve[q^3 (q - 2) - (h - (1/\[Epsilon])^2) == 0,
q, {h, 0, 2}]]
which returns
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Quartic equation: unable to match the limiting case
I am trying to solve the following quartic equation
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How to do a scatter point plot in 3D with 3 variables?
I am trying to solve this equation:
Solve[ ge r (5 (1 + fro) r^5 (-3 + 2 r) + fe^2 (20 Q^2 r^4 - 2 Q^4 L)) == 0, r]
for r and ...
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How to compute this infinite continued fraction?
I'm looking for a more efficient method to compute an infinite continued fraction frac[z,n] at a very high order — for example ...
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FindRoot inside FindRoot sometimes not working
I was trying to find the root of a function which is in-turn given only by the solution of FindRoot. The following does work for some values. For others it produces the same error as without the ...
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Solve symbolically for $u$ from $\sum_{i=1}^{n}\big(u\,x_i + y_i\big) = 0$
Trying Wolfram 14.3. It was with great surprise I saw the engine cannot symbolically handle Sum with a symbolic upper limit. I’m copying here the response I got ...
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Trouble finding Rational solutions to a simple elliptic curve equation
I have the following little code snippet.
SolveValues[{y^2 == x^3 - 2}, {x, y}, Integers]
Which correctly returns the solutions (3,5) and (3,-5).
However there ...
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Using FindRoot with several NIntegrate inside
I have the following system
$$-a_1^2 + 2 a_0 a_2 - 2 b_0 b_2 =0\quad \text{and } \quad a_2^2 - 2 a_1 a_3 + 2 a_0 a_4 - b_2^2 - 2 b_0 b_4 =0$$
where the following $a_i, b_i$ are integral of some ...
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NDSolve succeeds in Version 14.0.0.0, but later versions and renaming variables yields Power::infy
Main Question:
Why does NDSolve fail with Power::infy in Versions 14.3.0.0, 14.2.1.0, and 14.2.0.0,
yet succeeds in Version 14.0.0.0?
More troubling, why does NDSolve fail with Power::infy in Version ...
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Propagation of errors:
I am working on error propagation in Mathematica for a physics calculation involving tau lepton decay. I have a complex function that calculates the lifetime of the tau lepton based on various ...
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Non linear GPE With Imaginary Current Nonlinearity
I want to solve the Equation 22 and generate fig 3(a) given in the paper https://arxiv.org/pdf/1812.04672.
...
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How to Solve PDE using Inactive Form
I am trying to solve this PDE using the inactive form, however I ran into error stating that the: The PDE coefficient 0....
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Is there a built-in function or custom function that can perform symbolic solving under `GeometricScene` constraints？
In the new version of Mathematica, there is a new function called GeometricSolveValues that can solve for unknown geometric quantities in a geometric scene with ...
- 345
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Order of variables in the vars argument in Reduce function
My goal is to reduce two equations eq1 and eq2. According to the documentation, output of code1 condition for $V_{\text{eff}}(r)$ involves $m$. However, code2 doesn't involve $l$. It looks like ...
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How can I plot bifurcation diagrams given these isoclines?
I have the following system:
\begin{equation}
\begin{aligned}
\frac{dT}{dt} &= \frac{1}{\lambda} \Bigl(-a T^4 + b\big[1-(s_1 - s_0)e^{-\alpha_1 u}-s_0\big] \Bigr), \quad (1)\\[1ex]
\frac{du}{dt} &...
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Linear system of matrices
I don't know Mathematica very well, I have an equation involving matrices of the following form:
given two $5\times5$ matrices $A,B$ where $B$ is nilpotent we want to find a matrix $X$ such that
...
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Counting free variables in a system of linear equations
If we have a system of variables, say,
...
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Using NDSolve to solve three coupled ODEs
I am trying in this code to solve three non-linear ODEs together, and I want to plot the three functions as functions of η.
Why does my code not work?
...
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How to do this trigonometric calculation?
How to do this trigonometric calculation with Mathematica or Wolframalpha?
$$\frac{\sin a+\sin b}{\sin \left( a+b \right)}=m,\frac{\cos a-\cos b}{\sin \left( a-b \right)}=n,a\pm b\ne k\pi ,k\in \...
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Finding one non-negative solution to a system of linear equations
I need to find one non-negative solution to the system of linear equations
...
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The root neighborhood representation
I am trying to understand the content in the documentation for Root.
The root neighborhood representation Root[{f,c}] specifies ...
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Reducing with all variables belong to Real
I am trying to find v using Reduce in the equation G == (2*M*Pi)/(T*v^3). I set the domain to Reals to make v Real according to ...
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Usage of domain in Reduce [duplicate]
The goal is to find v. G, T, and M are constants. It's a simple question, but observing the output of Code1, there are three expressions included. Unlike Code1, Code2 is restricted domain to ...
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Help validating the solution to a nonlinear ODE: Does it solves other non-linear ODEs too? [closed]
I am working right now in this another question by doing examples and I got stuck in proving the results I found through Wolfram-Alpha are right.
The main differential equation is the following ODE:
$$...
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Generating Poincaré sections
I would like to reproduce the Poincaré sections presented in this and this papers, which look like
The figures are for energy values of E=0.2 (a) and E=0.25 (b) in the Hamiltonian, which reads
$$H=\...
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Why does NDSolve fail or slow down when simulating a driven JC model with time-dependent terms, even when the drive is off?
I'm performing a numerical check of an effective Hamiltonian transformation applied to a driven Jaynes–Cummings (JC) model. After applying a rotating frame transformation and rotating-wave ...
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Finding nonnegative solutions for systems of equations with parameters using constraints on parameters
Given
{c[0, 3, 4] + z[0, 2, 3] == c[2, 3, 4] + z[0, 2, 4],
y[0, 1, 2] + z[0, 2, 3] == c[0, 1, 3] + c[1, 2, 3],
y[0, 1, 2] + z[0, 2, 4] == c[0, 1, 4] + c[1, 2, 4]}
...
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Refine with Assumption or Assumming returns different results [closed]
To approach 1-dimensional collision problem, code 1 uses Refine and code 2 uses Assuming.
Question is:
As code1 and code2 below, ...
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Mathematica cannot solve {a==0,b==0,a c==0,b c==0}?
The title says it - when trying Solve[{a==0,b==0,a c==0,b c==0}] Mathematica works for quite a while without giving any output. I cannot get anything with the ...
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Trouble with "RegionMarker" in Mathematica FEM Package
I’m encountering issues while using the "RegionMarker" option to label different subregions in a mesh for solving PDEs with Mathematica’s FEM package (NDSolve/ToElementMesh). Despite ...
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The shortest path between two points in R^3 is a straight line. How can I find the coefficients for the equation of the line?
This is the system of equations; the points in R^3 are {x1,y1,z1} and {x2,y2,z2} and the coefficients are ...
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Wave equation via Laplace transform
Solve, via Laplace transforms
\begin{align}
w_{tt}&=w_{xx}\\
w(0,t)&=g(t), \lim_{x \rightarrow \infty}w(x,t)=0, \: x,t\geq 0\\
w(x,0)&=0=w_t(x,0)
\end{align}
where $w$ is the ...
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calculating and plotting tangents in mathematica [closed]
Compute the tangents to the graph 𝑓(𝑥) = 𝑥2 + 2 at the points 𝑥1 = 0 and 𝑥2 = 1.
(a) Plot the function 𝑓(𝑥) and the two tangents in a common plot.
(b) Determine the point of intersection of ...
