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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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Unable to solve/reduce GBM inequality

I am trying to solve a few inequalities like the one below for Z: S * Exp[(mu - sigma^2/2)*T + Sqrt[T]*sigma*Z] > k Manually,...
Phil-ZXX's user avatar
  • 471
1 vote
1 answer
149 views

Solving a complicated equation for approximate analytical solution

I am trying to solve the Following equation for r, 2*a*Q^4 + 5*r^4*(-4*Q^2 - 2*r*(-3*M + r) + 3*c*r^(1 - 3*\[Omega])*(1 + \[Omega])) ==0 Clearly this is unsolvable....
Debojyoti Mondal's user avatar
0 votes
1 answer
42 views

Using FindRoot inside Table [closed]

I want to use FindRoot inside Table to get solutions from several guesses. For one- variable non-linear equations this works well: ...
BolimboSHA's user avatar
0 votes
1 answer
71 views

Bifurcation plot of polynomial equation having two variable on y-axis and one variable on x-axis

I want to plot the following equation: ...
vijay's user avatar
  • 47
1 vote
1 answer
62 views

How to define a function as the Abs of a TransferFunctionModel?

Define a high pass filter first ...
metroidman's user avatar
5 votes
3 answers
208 views

Singularity or stiff system suspected in ODE that shouldn't have a singularity in the solution range

I am trying to numerically solve the following ODE where I know the value at p[1000]: ...
ydd's user avatar
  • 3,937
2 votes
1 answer
234 views
+100

Numerical Simulation of a Damped, Driven Nonlinear Wave System with Spatially Extended Initial Conditions

I am working on a project that requires creating a specific type of graph, but I am having trouble writing the correct code. The graph should look similar to the one I have attached below. Could ...
Athanasios Paraskevopoulos's user avatar
0 votes
0 answers
61 views

Solving a system of equations involving Gaussian integrals numerically [closed]

I wish to solve the following system of equations numerically in any software, I tried in Mathematica using the expectation functions, but I have a difficulty in understanding how to go about solving ...
rhombicosicodecahedron's user avatar
2 votes
1 answer
144 views

Why FindRoot gives wrong answer for the roots of a vector interpolation function

I've tried to use FindRoot to find the roots of a vector interpolation function, but Mathematica is clearly giving me the wrong answer. What's going on here? Here ...
xinxin guo's user avatar
  • 1,389
6 votes
3 answers
423 views

How many solutions does this system have?

Let us consider the system of two transcendental equations ...
user64494's user avatar
  • 26.7k
0 votes
0 answers
34 views

Solving a diffusion equation in a partially noisy potential

So recently I tried modelling diffusion over the rough part of a potential W. To do so I try numerically solving the Fokker-Planck equation: $$\partial_t P(x,t) = -\nabla\cdot J$$ $$J= -D(x)\nabla P-D(...
IronicOwl's user avatar
  • 115
1 vote
1 answer
74 views

Coupled pdes with two different derivatives

Can someone please help me with solving the following coupled equations for $m(x,t)$, $p(x,t)$, and $u(x,t)$, in an interval $0<x<5$? I found it very hard as the second equation has both x and t ...
questionerno8's user avatar
2 votes
1 answer
80 views

A first order differential equation: Inconsistent solutions by two approaches

Assuming $a>0,b>0,c>0$, in matrix A = {{a - I*b, c}, {c, a + I*b}}; I am interested in solving the following differential equation $\frac{d}{dt}R(t) = -i(...
phy_std's user avatar
  • 143
0 votes
1 answer
73 views

How does FindRoot work?

I have a system of 3 nonlinear equations in 3 unknown variables $f(x,y,z)=0, g(x,y,z)=0, q (x,y,z)=0$. I want to find $(x,y,z)$ that satisfies the 3 equation so I input: FindRoot[$\{f[x,y,z], g[x,y,z],...
Engineer's user avatar
  • 119
2 votes
0 answers
39 views

Stop NSolve after a certain amount of time and return calculated solutions

I am trying to solve a system of equations of the form: ...
A P's user avatar
  • 203
0 votes
0 answers
26 views

Using absolute values as initial conditions

I have a system of equations I want to solve using NDSolve, which is ...
Jules Alvarez's user avatar
0 votes
0 answers
48 views

Stabilise equations for motion of Inextensible string subject to spatially non-uniform forces

I would like to simulate the motion of an inextensible membrane in 1D as an inextensible string subject to spatially-dependent body forces. For now, I would like it to be constrained at both ends. I ...
Ariana Fenris's user avatar
3 votes
1 answer
62 views

Solving a first order linear matrix differential equation

I am struggling in solving the following differential equation (with B and g real numbers) ...
phy_std's user avatar
  • 143
0 votes
1 answer
63 views

Vortex beam profile plot [duplicate]

I want to plot this type of plot for the Lagurree Gaussian beam $\begin{aligned} u(r, \phi, z)= & C_{l p}^{L G} \frac{w_0}{w(z)}\left(\frac{r \sqrt{2}}{w(z)}\right)^{|l|} \exp \left(-\frac{r^2}{w^...
Himani Juneja's user avatar
1 vote
0 answers
63 views

Numerically solving coupled 2rd ODE with tiny numbers

I am solving the initial value problem of two coupled ODEs numerically. The equations are ...
Link's user avatar
  • 31
0 votes
1 answer
69 views

How to get the value of expression if I have some equalities?

I have this system of equations: ...
Antoine Russ's user avatar
2 votes
4 answers
145 views

Solving equation analytically

I was going through an article. I have the following functions, f[r_] := 1 - (2*M*r^2)/(r^3 + g^3) + (8/3)*Pi*P*r^2 v[r_] := f[r]/r^2 Now I want to solve ...
Debojyoti Mondal's user avatar
3 votes
2 answers
140 views

Plotting Phase Portrait of Duffing Equation

I study a paper that describes a stationary problem where the function $\Phi_d$ satisfies the boundary conditions and is governed by a modified Laplace equation with a non-linear term. Here's a ...
Athanasios Paraskevopoulos's user avatar
-2 votes
1 answer
53 views

How to find the Proportion? [duplicate]

How to find the Proportion? Clear["`*"] a = 2 k; b = 3 k; c = 4 k; k > 0; (a + b) : (b + c) : (c + a) How can I get this result? ...
csn899's user avatar
  • 4,315
1 vote
2 answers
96 views

I can't get NSolve to work

I have defined the function ekert the following way; ...
Dotman's user avatar
  • 456
4 votes
1 answer
209 views

Is there any way to get DSolve to provide trivial solutions?

When trying to solve DSolve[{x''[t] + x'[t] == x[t] y[t], y''[t] == -x[t] y[t]}, {x, y}, t] Mathematica returns the input. Two solutions (trivial) are $$(x(t),y(...
Moo's user avatar
  • 3,334
2 votes
1 answer
85 views

How to solve the integro - differential equation with complex value involved?

I am trying to solve the PDEs which contains Integro-differential and complex values. For example, the following PDE can be easily solved. ...
sixpenny's user avatar
  • 149
3 votes
3 answers
97 views

How to invert a series with two variables, where the series is expanded in the other variable?

I have defined an expression that is a series in powers of $1/c$: ...
Christopher's user avatar
3 votes
1 answer
107 views

Why does singular solution not satisfy the ode?

Should not singular solution also satisfy the ode itself? Since it is a solution. Why does Mathematica V 14 in this example generate a singular solution which does not seem to satisfy the ode itself <...
Nasser's user avatar
  • 145k
1 vote
1 answer
90 views

NDSolve fails first order ODEs, but works when transformed to second order [duplicate]

The short version is that I am trying to solve a relatively simple system of coupled first order ODEs with NDSolve in Mathematica 12.1.1.0 on Windows. This system ...
Alexander Erlich's user avatar
3 votes
0 answers
68 views

Inconsistent solutions in two representations

Consider the following differential equations: ...
phy_std's user avatar
  • 143
3 votes
1 answer
106 views

How can I solve this inequation over positive integers?

$$2023^i + 2023^{101-i}(-1)^i < 0, \quad i\in \mathbb N^+$$ My code: Reduce[2023^x+2023^(101-x)*(-1)^x<0 && x ∈ PositiveIntegers, x] gives an error ...
neo742's user avatar
  • 45
2 votes
2 answers
136 views

Plotting 3x3 Linear System

I am trying to plot the following linear system ($3\times 3$) in different ways. My question is what wrong have I done to my last code? ...
Athanasios Paraskevopoulos's user avatar
0 votes
1 answer
60 views

NIntegrate inside FindRoot has evaluated to non-numerical values

I have a function Fdiff[m] that I want to put in FindRoot. However, it has given me an error saying that the integrand has ...
mathemania's user avatar
3 votes
2 answers
137 views

How to divide a known root out of a polynomial?

Consider this simple 5th order polynomial: pol=x^5+x^4+1 Factor[pol] (* (1+x+x^2)(1-x+x^3) *) root=FindInstance[pol==0, x] (* -1/2 -I/2 Sqrt[3] *) ...
Jos Bergervoet's user avatar
5 votes
3 answers
363 views

How to get the analytical form of a solution to an algebraic equation?

The real analytical solution of the algebraic equation $x^5 + 10 x^3 + 20 x == 4$ is $x=-2^{2/5} + 2^{3/5}$, how to get it with Mathematica? I've tried with ...
SHBooKP's user avatar
  • 370
1 vote
2 answers
70 views

Solution of $x=0$ for $\frac{4 x^2 (5 + x)}{20 x + 4 x^2} = 2 x$? [duplicate]

The equation in question here is $\frac{4x^{2}\left(5+x\right)}{20x+4x^{2}}=2x$. Why does Mathematica (13.1) return x->0 for this? The left side is undefined at ...
CommonerG's user avatar
  • 111
0 votes
1 answer
142 views

Solving coupled quasi-linear PDEs with boundary conditions

I realized that in this solution, changing one of the boundary conditions makes the answer invalid. I wonder if it is possible to modify the code in this answer to solve the following equations. $$ \...
questionerno8's user avatar
-2 votes
2 answers
64 views

How to convert the form of the Solve solution to the form of the Reduce solution

{tanx -> 1/Sqrt[2], tanx -> -Sqrt[2]} How to convert the form of the solve solution above to the form of the reduce solution ...
csn899's user avatar
  • 4,315
-1 votes
2 answers
112 views

Why does this system of trigonometric equations have no solution? [closed]

Clear["`*"] Reduce[{Sin[x] + Sin[3 x] + Sin[5 x] == 1, Cos[x] + Cos[3 x] + Cos[5 x] == Sqrt[2] + 1, tan3x == Sin[3 x]/Cos[3 x]}, tan3x, {x}, Reals] ...
csn899's user avatar
  • 4,315
1 vote
2 answers
82 views

Ordering of solutions of NSolve

I want to compute the solution to an equation with a parameter. It turns out that this solution is a sextic polynomial and mathematica outputs the solutions in a root form. Here's my code ...
Geigercounter's user avatar
2 votes
1 answer
224 views

Mathematica yields repeated solutions when only one exists

The equation is: x Log[x] - 3/2 x - 1/(2 x) + 2 == 0 Its root is just one, which is 1. Why does the output repeatedly write out 1 multiple times? ...
csn899's user avatar
  • 4,315
2 votes
2 answers
138 views

How to solve a matrix differential equation $\frac{d X}{dt} = i(X Y- Y^\dagger X)$?

In eq (21) on page-5 of this article, we have matrix HEP = (\[Omega]/2)*{{-2*I, 1}, {1, 0}}; and I am interested in finding matrix ...
User101's user avatar
  • 613
1 vote
0 answers
66 views

Problems with implementation of subresultant pseudo-remainder sequence in Sturm's theorem

I've implemented the subresultant pseudo-remainder sequences ( https://en.wikipedia.org/wiki/Polynomial_greatest_common_divisor#Pseudo-remainder_sequences ) as described in Wikipedia. However, when ...
Moonwalker's user avatar
0 votes
1 answer
43 views

How can we constrain this set of equations to obtain the desired form?

How can we constrain this set of equations to obtain the desired form? Solve[{(y0 - y)/(x0 - x) *-a/b == -1, a*(x + x0)/2 + b*(y + y0)/2 + c == 0}, {x, y}] get ...
csn899's user avatar
  • 4,315
2 votes
2 answers
175 views

How to solve differential equation with small values

I want to solve this system of differential equations with Mathematica: ...
Jules Alvarez's user avatar
1 vote
0 answers
81 views

How to decrease the computation timing while using NIntegrate?

I'm trying to calculate the $A$ and $F$ values by using this code, ...
Entangled Quark's user avatar
0 votes
0 answers
42 views

Solve in solving equation system

I have the following problem: I have a system of equations specifically consisting of 56 equations, with 34 coefficients to be determined, in simplified form: ...
iron's user avatar
  • 1
0 votes
1 answer
71 views

Optimization for NSolve

I am trying to solve the system of n equations numerically. Basically, I am solving saddle point equations for eigenvalues of hermitean matrices and trying to reproduce Wigner's semicircle law: ...
Prokopii Anempodistov's user avatar
0 votes
1 answer
51 views

How to verify an elliptic function solution of PDEs and interpret its verification results?

I am sorry that I can't give you my whole code here, its too long and my mathematica version is 13. Here is the partial differential equations, $$ \left.\left\{\begin{array}{c}u_t-3qu^2u_x+\frac{3}{2}...
godspeed's user avatar

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