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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Avoid imaginary result FindRoot
I have a code where I'm using FindRoot for the equation toroottp. I plug in some sample values on ...
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Change value of a single input variabe to get out put results for each case the input single value is changed
I would like to put random values like (s = 0.1, 0.7 , 0.4, 0.15, 0.18) to get the output results which are ( X and Rn ) for these values in different excel files or in the same excel file ,instead of ...
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Roots of a transcendental equation with unknown a complex number
I am trying to solve a problem and I got stuck with a complicated transcendental equation. I intend to find these roots. Here, $\omega$ is a complex number, whose imaginary part can be positive or ...
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Reduce or Limit to have positive value!
I would like to see where this function is positive ??!!
Reduce[{Tanh[x]/Sqrt[-1 + Tanh[x]^2] > 0}, x, Reals]
thank you.
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NSolve just spits out the input functions
I was trying to solve 3 equations with 3 variables with NSolve, however, NSolve didn't really do anything but spitting out the ...
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How to take a derivative of a function with respect to another function inside the function?
I have these two equations:
...
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194
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Solving symbolically a trascendental equation containing an exponential
Is it possible to solve symbolically this equation for $x$: $$\exp \left(-x^2\right)=\frac{c_1}{\sqrt{c_2-c_3 x}}$$
Exp[-x^2] == c1/Sqrt[c2 - c3 x]
$c_1$, $c_2$ ...
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Plot for DSolve in mathematica [closed]
I don't Plot it's not working!!, can you help me?
...
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549
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My model has not finished evaluating in more than a day so can't test if it works, what is wrong with it?
Hello I have this modified monocentric city model that I have been working on for a while.
Sorry for the long post, I wanted to add the whole code, because it's all connected.
My suspicion is that it ...
3
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3
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Finding 3d circle center
Num calcn for Tria Center
Can someone please help in finding an analytic expression for the center of a circle through 3 given points by modifying ( Solve in place of NSolve ) a conventional numerical ...
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Numerical Plot for an example
I would like to compare the numerical and analytical solution with plot for this example but something is wrong I don't know how to fix it?!!
...
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Identifying the intersection between a ConditionalExpression and a parametric curve
I'm trying to determine the intersection of lines over a surface (if they exist). My problem is that one of the lines is defined as a conditional expression and for the others I only have a parametric ...
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Warning: Inconsistent or redundant transcendental equation
When I try to solve (for complex c[i,j])
...
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How to find All Solution of a equation? [closed]
How to get ALL solutions of the equation tanh x = 135 x. What is the command?
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162
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Numerically solving transcendental equation for a range of values
I'm new to Mathematica, and I'm trying to solve for corresponding Ef values for a range of T values in the transcendental equation: p = n + Nd.
hbar = 6.5821*10^-16
...
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How to solve 2D eigenvalue problem with robin boundary conditions
I need to solve an eigenvalue problem in 2D as seen in the picture.
I've tried the function NDEigensystem but reading its documentation it seems it has issues with ...
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Solving a nonlinear integral equation
I wonder if Mathematica can be used to numerically solve the following nonlinear integral equation?
$\lambda^2(t)-\frac{1}{\lambda^4(t)}+\frac{2}{R_0^2} \int_{R_0}^{R_0+u_0t} R \left[\frac{\lambda^...
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Can Mathematica solve an ode asymptotically as x goes to infinity?
Given the following ode for $x\rightarrow\infty$:
$$\left(x f(x)^3 \left(\frac{(x f^\prime)^\prime}{x}\right)^\prime\right)^\prime=0,$$
in the sense of "asymptotics", the equal sign is ...
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Why Solve is not working? [closed]
I'm new here and I'm a newbie also with Mathematica, so probably this an easy and stupid question. If you have suggestion on how can I learn at least the basics of the language, I appreciate it.
I'm ...
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Redundancy in Solve
Solve[{
a[1] a[2] == a[3] a[4],
a[1]^2 == a[4]^2,
a[1] a[3] == a[2] a[4],
a[2]^2 == a[3]^2
}]
returns
...
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Solve a symbolic expression
I'm working with the Hoek Brown plastic yield surface to model soil/rock materials.
The yield surface is given by:
Were sig1 and sig3 are the maximum and minimum principal stresses. sigc, m, s and n ...
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Theory behind CountRoots
According to this page, one can compute the number of zeros of a meromorphic function over an interval in Mathematica.
I am working with univariate functions of x, which are meromorphic elementary ...
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1
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How can I solve a PDE on the real line with DSolve? [closed]
I would like to know if it is possible to solve a PDE on the real line by using DSolve.
For exapmle cosider the heat equation $u_t=u_{xx}$, $u(x,0)=e^{-x^2}$
for $x \in \mathbb{R}$
the code I tried ...
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4
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Solving equation over TruncatedDistribution (FindRoot)
I'm trying to solve the following equation :
...
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Looking for a efficient way of solving a matrix which is function of some variable
What is the efficient way to solve the matrix having a dependency on some varaible f. I have a simple matrix g which is ...
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Rational roots of x^5 + a x + b
I'm validating a formula from these article:
https://www.annals-csis.org/Volume_20/drp/pdf/164.pdf
https://people.math.carleton.ca/~williams/papers/pdf/185.pdf
If irreducible rational equation $x^5 +...
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Mathematica not giving real roots when computing roots of cubic equation [closed]
Here's the code and corresponding output
soln = NSolve[
541.5535677 == (1/V) + (1.57x10^-4/V^2) + (9.56x10^-3/V^3), V]
{{V -> -0.0124127 - 0.0225339 I}, {V -> -0.0124127 +
0.0225339 I}, {V -&...
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4
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Solving Burger's equation with NDSolve at large time
I want to solve the following Burger's equation
$$\partial_tu+\partial_x\left(\frac{u^2}{2}\right)=0,~~x\in[0,2\pi],~t>0\\u(x,0)=\frac{1}{3}+\frac{2}{3}\sin(x)$$
with mathematica. Here's my code:
<...
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Express rational and infinite expressions in Mathematica [closed]
I have several doubts about notation. I would appreciate any clarifications.
a) I can express, for example, a periodic or semi-periodic number without writing it in its rational form. Can such ...
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Symbolic PDE manipulation
I'd like to transform a PDE in a way such that I can express a temporal derivative as a spatial derivative using some known relation.
Very simple example:
...
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Get the correct branch form Solve
I am reproducing the derivation in this article (exploration of a family of circles centered on an ellipse).
I only need the outer curve, the results obtained from Mathematica are more complicated ...
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1
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Help with equation within adjacency matrix
(Value R seen within desired matrix equation)
resistance = 0.5;
(L = ???)
identitymat = IdentityMatrix[30];
fullmatrix = ((AdjacencyMatrix[plot])) + identitymat // MatrixForm
p.s. I believe I have ...
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How do we just have $\log$ solution?
Mathematica solves this but I want the solution just as Ln[..]?!!
DSolve[y'[t] == 3/2 a*y[t] ((y[t] + b)^2 - f), y[t], t]
thanks
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Solving multivariable trig Identities
I'm trying to solve for a certain set of trig identities in terms of other trig identities. I saw this and this, but in my example, I have two tries:
...
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Is it possible to solve a differential equation with a user-defined variable mesh in NDSolve?
For some differential equations, its solution may evolve to a cusp, for example, singular behavior. One may want to introduce additional mesh points near the cusp to accurately follow the solution ...
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Why is Solve not able to solve the following system of coupled non-linear equations?
I have the following two coupled non-linear equations
...
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How to analytically solve for an intersection of two functions on an interval?
I would like to analytically solve for the intersection of two functions on a given interval and store the solution as a function (of parameters) for later use. How can I tell Mathematica to look for ...
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Resolve ForAll does not work while FindInstance does not find any counter example
I have some implication equations. need to check and verify, so i used Resolve forall. but it just returns me the same relation, seems does not work or a problem exists. so then I tried to find if ...
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What is the fastest way to check whether a cubic equation is solvable in integers?
My code needs to check whether a lot of low-degree equations (usually quadratic and cubic) are solvable in integers. There are many equations, so the speed is crucial. Let us start with quadratic ...
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Convergence plot of Lyapunov exponents
I am trying to reproduce the convergence plot of the four Lyapunov exponents for a string from this paper (page 12, figure 7).
The code that I have used till now to find the equations is given below:
<...
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Techniques to solve complicated simultaneous equations
I want to solve 5 equations simultaneously for 5 variables (N2[t],TT[t],PP'[t],SS'[t],z1'[t], code attached at the end of the post).
The equations are extremely long and complicated. I have tried ...
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3
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Solving equation with delay term
I am trying to solve an equation looks like this...
x[t] == t^2 + x[t-10]
How can I obtain a numerical solution for x[t] in Mathematica?
Thanks.
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Poincare section for a perturbed string
I am trying to find the Poincare section of a perturbed string in a gravitational background with a magnetic field. The plots that I am trying to reproduce are from this paper (page 11).
The code that ...
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How to find multiple zeroes of a single function
This is the problem I am solving.
I have defined my wanted equation as it is shown on the picture. Finding the first 0 (root) is not difficult with using FindRoot function.
The problem that i am ...
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Partial Differential equation initial condition [closed]
For the equation $u=xu_{x} + yu_{y} + \dfrac{1}{2}(u_{x}^{2} + u_{y}^{2})$ find a solution with $u(x,0)= \dfrac{1}{2}(1-x^{2})$
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Reduce yields ArcTan instead of Pi/4
I expect this call:
Reduce[Sin[x] - Cos[x] == 0, x, Reals]
to return
$x = \pi/4 + 2k\pi \ \vee \ x = -3/4 \ \pi + 2k\pi$.
However, $\pi/4$ and $3/4\ \pi$ get ...
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