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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7
votes
2answers
162 views

DEigensystem gives x-dependent eigenvalues

Bug introduced in Version 11 or earlier and persisting through 12.1. Reported to Wolfram Technical Support as CASE:4532301. I am considering the eigenvalue problem associated with the double-well ...
0
votes
0answers
64 views

3 dimensional Laplacian with 4 non-homogeneous boundary conditions

I have the 3-D Laplacian ($\nabla^2 T(x,y,z)=0$) defined over $x\in[0,L], y\in[0,l], z\in[0,w]$ with four non-homogeneous boundary conditions as follows: $$T(0,y,z)=t_{hi}\tag1$$ $$T(x,0,z)=t_{ci}\...
2
votes
1answer
54 views

I need help solving this hyperbolic equation [duplicate]

I have some data and I'd like to calculate the radius of curvature. The formula is: $$R_{oc}\space Sinh\left[\frac{D_{LSS}}{R_{OC}}\right]=\frac{s_*}{\theta_*}$$ Noting that $s_*$ is sh, $\theta_*$ ...
0
votes
1answer
88 views

Output of CoefficientRules into Jacobian matrix

I have a pair of large polynomials in u, v, a1...a9 and b1...b9, generated by ...
0
votes
3answers
460 views

Problems with finding the real solutions of equation [duplicate]

I am trying to find real solutions of equation using Mathematica 8.0 but there is some problem I don't know how to explain. For example, for the input ...
2
votes
0answers
37 views

NDSolve for closed-loop system with Unit Delay (attempt to compare with Simulink) [closed]

I'm trying to reproduce a scheme from Simulink with a unit delay. To do this, I use the NDSolve command with an additional equation that implements a unit delay loop. The results do not match, and I ...
2
votes
0answers
26 views

How to plot the parametric plot of two linear time dependent equation with two variables? [closed]

I am trying to plot the parametric plot between P1 and Q1. For this, I am using the code written below. I don't know where I am doing wrong. I think there are imaginary terms creating problems but is ...
1
vote
1answer
86 views

How to calculate unknown function in a equation analyticaly? [closed]

I want value of u1 in terms of T1. How i will be abel to do this? ...
1
vote
0answers
53 views

Integration resulting in imaginary result while solving a boundary value problem

I am trying to solve a boundary value problem involving a three-dimensional Laplacian $\nabla^2T(x,y,z)=0$ on the domain $x\in[0,L], y\in[0,l], z\in[0,w]$. I have six boundary conditions and based on ...
7
votes
1answer
390 views
2
votes
1answer
45 views

How can I find whether a given algebraic expresion T can be obtained as linear combination from a set S (with number coeficients)

We might take: s = {(x-y)^2, x*y+z}; e = (x+y)^2 + 4*z; and linearDecompose[e,s] could give ...
0
votes
0answers
38 views

Mathematica has letters that are already defined with certain attributes that cannot be changed?

I want to solve a system of equations to find derivatives of sixth order with finite differences. It's easy for me to define g as the function fi and ...
0
votes
0answers
45 views

Code running in Mathematica 12.0 but not in 11.3

When I run the following code in Mathematica 12.0, it doesn't cause any problems but for Mathematica 11.3 it gives General::munfl error ...
8
votes
1answer
681 views

DSolve with SetOptions[Solve, Method -> Reduce] Behaving Differently in Ver 11.1.1

With version "11.1.1 for Microsoft Windows (64-bit) (April 18, 2017)", DSolve[{SI'[s] == Sin[PH[s]] , PH'[s] == Sin[SI[s]]/e}, {SI[s], PH[s]}, s] produces the ...
4
votes
1answer
271 views

Approach to analytically solve a Coupled system of PDE in Mathematica [Heat transfer in cylindrical coordinates]

I have the following two PDEs, which describe steady-state coupled heat transport between a externally heated axi-symmetric solid body (Eq. 1, $T(r,z)$) and a fluid (Eq. 2, $t(z)$) flowing inside it $...
0
votes
0answers
56 views

How to resolve probabilities over natural numbers?

Given a simple function f: f[n_, b_] := Mod[n, b] How to compute the probability of ...
0
votes
1answer
31 views

Use the NSolve function on a list of values

Is there a way to have NSolve loop through a list of values? I know how to use it for single values but unsure if I can get it to loop through a list. I want it to loop through my list of p and have ...
0
votes
1answer
59 views

`FindRoot` : Root varying wildly with initial guess

I am trying to obtain a plot between two variables related through an equation as follows : ...
0
votes
1answer
137 views

FindRoot::lstol error

I'm getting the message: FindRoot::lstol: The line search decreased the step size to within tolerance specified by AccuracyGoal and PrecisionGoal but was unable to find a sufficient decrease in the ...
0
votes
0answers
46 views

Does Solve work with symbolic tensors?

I am considering the usefulness of Mathematica's symbolic tensors to handle algebra which I encounter in acoustics of solids. Is there a way to solve equations written in symbolic tensors? This is ...
0
votes
1answer
46 views

Get the representation of {x,\theta} with the given equations

I am working with a Transfer funtion problem. I want to get the representation of {x, $\theta$} with the given equtions(below). In the equation x10 and x20 means the initial value of x1 and x2. all ...
1
vote
1answer
41 views

I need help solving an ODE for a range

I've got an ODE which gives me the proper form of a solution: ode = 0 == -(c + A*t)^2 + D[r[t], t]^2; sol = DSolve[{ode}, r[t], t] The solution is: ...
0
votes
0answers
25 views

SolveAlways set

I have a SolveAlways command: SolveAlways[x==1,y] (This is a minimal solution, the acutal one is a lot harder) The output is ...
0
votes
2answers
47 views

Solving simultaneously some equations [closed]

I have some equations (18) and want to obtain a variable (X7) simultaneously for all equations by NSolve or Find Root. but I can not. Any one can help me? my equations ...
0
votes
3answers
143 views

Non-linear equation of functions

I would like to solve (I think with NSolve, but I am not sure) and plot the function $w(z)$: the relation contains other known functions dependent on $z$, which are ...
1
vote
3answers
142 views

Solving equations involving integrals

I need to find the value of $z$ for a particular value of $D_c$ (eg. $500$), but $z$ is inside an integral, and I'm not able to use Solve since the integral is ...
8
votes
3answers
568 views

How can I make Mathematica solve this set of four equations?

I use Mathematica version 12.1 on Windows 10. I have four equations in four unknowns. Is there a trick to make Mathematica solve these? I tried Solve and <...
0
votes
1answer
40 views

Why does restricting the domain not eliminate this solution?

Beside this specific problem I'm wondering if there's a more explicit way that I can understand when Solve and Reduce will find solutions. I find myself repeatedly getting stuck where I'll get ...
0
votes
1answer
44 views

Solve Unable to Solve with Inexact Coefficients [closed]

I am trying to find fixed points for a set of 3 differential equations by setting the first derivatives to zero. I plug these equations into Mathematica's Solve[] function like this: ...
1
vote
0answers
56 views

Longitudinal Bar Vibration & Boundary Condition Problems

I am trying to solve the PDE for longitudinal vibrations in a bar (as shown for example at Youtube Longitudinal Bar Vibration). My challenge is the application I am trying to solve has these boundary ...
-2
votes
1answer
82 views

Could someone show me how to solve a differential equation in Mathematica? [closed]

I have the following equation: $$A^2\space t^2\space dt^2=-c^2\space dt^2+\frac{dr^2}{1-K\space r^2}$$ I understand how linear equations are solved in Mathematica, but can someone walk me through the ...
1
vote
1answer
30 views

How to assign a value from the outcomes of Solve or 0?

Here is my problem: I want to achieve a loop and assign the outcomes of Solve to variables for future use. But the equations in Solve may have no solutions. Under this circumstance, I want to assign ...
1
vote
1answer
34 views

Plot solutions of NSolve with multiple variables in different colors

I'm trying to plot the solutions of a set of equations in dependence of a parameter. Say my variables are vars = {x,y}; and the system I want to solve is ...
2
votes
3answers
76 views

Four equations and four unknown variables in Mathematica

I'm trying to solve a problem in Mathematica where I have 4 unknown variables and 4 equations, but it doesn't quite work for me. I would appreciate if someone could tell me what I'm doing wrong. <...
1
vote
3answers
62 views

Loosen tolerances to get a solution from NSolve for trig system

This is more an exercise in learning Mathematica than a real issue because the solution for me is just to solve half of the system. I have a simple system of trig equations and can't solve the angle, ...
1
vote
1answer
67 views

I am unable to solve angle of a trigonometric equation

I am fairly new to Mathematica, so this may be a simplistic question, but I want to learn. I know how to use the Solve function to solve a single equation like this: $$\cos[41.614-x]-1.2752|cos[1....
1
vote
2answers
153 views

What is LyapunovSolve::meig message about?

According to Wikipedia, a Sylvester equation $AX+XB=C$ has a unique solution for $X$ exactly when there are no common eigenvalues of $A$ and $-B$. But the following code gives me a message I don't ...
2
votes
1answer
44 views

Equating both sides of the equation [closed]

I want to verify that two equations are equal. I have comparing the left and right hand side, which should print 1 or 0, but it doesn't work, it just re-prints the equations.
0
votes
1answer
52 views

Grid for NDSolve

i want to get the output of NDsolve in the form of a tbale/grid that can be exported to .xls/.csv. NDSolve[x'[t]==Exp[t], y'[t]==cos[t], x[0]=0, y[0]=1,{x[t],y[t]},{t,0,10}] I am expecting an output ...
1
vote
1answer
140 views

Partial differential equation - DSolve gives no output, but solution exists

I have trouble obtaining solution for equation using DSolve: My mathematica code is given by: ...
2
votes
1answer
40 views

Find unknown parameters from NonLinear fitted data

I obtained the fitted model from the image using the following code: ...
6
votes
2answers
1k views

Lyapunov exponent of Delay Differential Equation

I have a Delay Differential Equation as given below ...
4
votes
2answers
140 views

How to solve trisecting a pentagon

I thought maybe I could learn Mathematica to help me trisect a pentagon. I can't figure out how to write a Solve to get d0 on <...
0
votes
1answer
36 views

Is there a simple way to move all terms with $x$ or $y$ in the LHS and all others in the RHS of an equation?

I did the following: In the last equations, is there a simple way to move all terms with $x$ or $y$ in the LHS and all others in the RHS?
1
vote
2answers
67 views

Looking for (possibly) two roots with FindRoot

I am looking for intersections of the a family of functions $F_n(k)$ defined over $[0,1)$ $$\frac{2K(k)n}{\frac{1+k}{\sqrt{1+k^2}}} $$ where $K$ is the complete elliptic integral of the first kind, ...
0
votes
0answers
18 views

Problem replacing an ansatz in a field equation with spin-isospin matrices

I've been lately trying to replicate a calculation but it is not working. The main problem is simple. I just have to replace an ansatz in a equation, that is (sorry for putting an image of that ) ...
1
vote
0answers
103 views

How can I get better results using DSolve?

I am solving my fourth-order differential equation by using DSolve. When I solved it gives me an error related to precision. How can I improve my results and get better output? Any help will be ...
1
vote
1answer
43 views

Solving trigonometric equations

I need to solve these three trigonometric equations, and figure out the a, b and c. But, this takes too long time, and I am not sure the answer is right. Thus, How can I progress my code to speed it ...
1
vote
1answer
56 views

How do I use Solve to find a variable in the integral?

I have the following formula: $$t(a) = \frac{1}{H_0}\int_0^a \frac{da'}{\sqrt{\Omega_{r,0}a^{-2} + \Omega_{m,0}a^{-1}+\Omega_{\Lambda,0}a^2 + (1-\Omega_0)}}$$ I want to go in the opposite direction. ...
0
votes
1answer
46 views

Evaluating beyond the range `PlotRange` can

I am having an equation which I want to plot. ...

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