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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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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1 answer
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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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4 votes
1 answer
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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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How to solve a problem with inequality

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1 answer
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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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1 vote
2 answers
82 views

Why can't the two variables' equations be solved?

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0 answers
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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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2 votes
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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 answer
51 views

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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5 votes
4 answers
200 views

Solving equation over TruncatedDistribution (FindRoot)

I'm trying to solve the following equation : ...
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4 votes
2 answers
71 views

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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5 votes
1 answer
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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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1 answer
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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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9 votes
4 answers
706 views

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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1 vote
2 answers
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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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2 votes
1 answer
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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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1 vote
1 answer
72 views

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 answer
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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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1 vote
1 answer
68 views

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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1 vote
1 answer
64 views

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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3 votes
1 answer
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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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1 vote
1 answer
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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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0 answers
39 views

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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0 answers
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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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3 votes
1 answer
103 views

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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2 votes
1 answer
129 views

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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2 votes
1 answer
100 views

Strange error in FindInstance result

I was running the following code ...
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1 vote
1 answer
99 views

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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2 votes
3 answers
148 views

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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5 votes
1 answer
243 views

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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1 answer
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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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-1 votes
1 answer
42 views

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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2 votes
1 answer
74 views

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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1 vote
2 answers
81 views

Using Loop to find a specific Energy

I am given a Hamiltonian: ...
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1 vote
1 answer
58 views

Finding Hamiltonian from a perturbative Action

I am given a perturbative action $$\frac{S}{\mathcal{T}}=\int dt\sum _{n=0,1} (\dot{c_n}{}^2-c_n^2 \omega _n^2)+7.11 c_0^3+35.3 c_0 c_1^2+4.66 c_0 \dot{c_0}{}^2+1.32 c_0 \dot{c_1}{}^2-7.57 \dot{c_0} ...
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0 votes
1 answer
101 views

Mathematica doesn't solve linear system of equations that emerges from finite difference method [closed]

I want to solve the ODE $$u''(x)+u(x)=e^{-x^2}$$ $$u(0)=u(10)=0$$ using finite difference method. I divide the interval $[0,10]$ uniformly by $x_i=0+ih$ using step size $h=\frac{10}{11}$. By ...
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-3 votes
0 answers
86 views

Plot from Numerical solving

I was working on this code to get some plots but it doesn't want to work?!!! ...
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-1 votes
1 answer
90 views

Solving System of Nonlinear Equations

My question is fully contained in the image below - for some reason StackExchange wasn't letting me post it due to some unknown formatting issue so I simply took a picture and attached it below. ...
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6 votes
3 answers
312 views

Neglecting higher order terms in a Lagrangian

I have a lagrangian which is modified by variable change. I want to neglect all the 4th order and higher terms in the new lagrangian. The code being used is given below: ...
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7 votes
9 answers
769 views

What is an easy way to transform an equality into a replacement rule?

I found the necessity for the following procedure and was surprised I couldn't find a built-in function to do the following. I include my solution in case someone needs the same functionality, but if ...
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0 votes
2 answers
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Solving System of six Non-Linear Equations in Six Unknowns

I've been trying to solve the following system of equations using NSolve and the code has been running for close to 24 hours already. Is this normal? Is there a quicker way to solve these equations? ...
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1 vote
2 answers
79 views

How to find that this be always real number

I don't know how to find out this is be real number for l[y]? ...
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4 votes
2 answers
135 views

Rewriting algebraic expressions as combinations of other expressions

I would like to write x^5 + 1/x^5 in terms of x^2 + 1/x^2, x^3 + 1/x^3 and ...
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0 votes
1 answer
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Finding the roots of a quartic [closed]

I try to find the roots of $f(x)=x^4+(4a-2)x^3+(6a^2-6a)x^2+(4a^3-7a^2)x+ a^4-2a^3 =0$ with $0<a<1$. How do i get with Mathematica all solutions (general expressions, real and complex)? With <...
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5 votes
2 answers
254 views

How to pose simultaneous trigonometric equations problem in a way solvable by mathematica

Context: A camera at O has an image of a rectangular object ABCD. From the 2D coordinates of the image + the projection matrix of the camera I can calculate the direction vectors $\hat {A}, \hat{B}, \...
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0 votes
0 answers
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Simplification of long trigonometric expression taking a long time

I have tried to Simplify as well as FullSimplify a long trigonometric expression to get a simplified form of the expression but it takes a very long time almost hours and sometimes it also shows error ...
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2 votes
0 answers
86 views

How to solve this equation analytically?

Why can't Mathematica 13 solve this equation in radicals? Solve[x^5 - 5*x^4 - 10*x^3 - 10*x^2 - 5*x - 1 == 0, x] // ToRadicals I also tried to use ...
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2 votes
2 answers
96 views

Evading the fewer dependent variables than equations error

I'm writing a code that tries to solve differential equations generated from some existing code. The equations so generated are often seemingly overdetermined but actually solvable: e.g. ...
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