# 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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### 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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### 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 -&...
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: <...
1 vote
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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 ...
52 views

### 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: ...
1 vote
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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### Help with equation within adjacency matrix

(Value R seen within desired matrix equation) resistance = 0.5; (L = ???) identitymat = IdentityMatrix; fullmatrix = ((AdjacencyMatrix[plot])) + identitymat // MatrixForm p.s. I believe I have ...
1 vote
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
1 vote
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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 ...
1 vote
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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 ...
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 ...
25 views

### 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 ...
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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### 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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### Strange error in FindInstance result

I was running the following code ...
1 vote
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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 ...
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.
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 ...
70 views

### 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 ...
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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### 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 ...
1 vote
81 views

### Using Loop to find a specific Energy

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

I am given a perturbative action $$\frac{S}{\mathcal{T}}=\int dt\sum _{n=0,1} (\dot{c_n}{}^2-c_n^2 \omega _n^2)+7.11 c_0^3+35.3 c_0 c_1^2+4.66 c_0 \dot{c_0}{}^2+1.32 c_0 \dot{c_1}{}^2-7.57 \dot{c_0} ... 0 votes 1 answer 101 views ### Mathematica doesn't solve linear system of equations that emerges from finite difference method [closed] I want to solve the ODE$$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 ... 86 views

### Plot from Numerical solving

I was working on this code to get some plots but it doesn't want to work?!!! ...
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. ...
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: ...
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 ...
110 views

### 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? ...
1 vote
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### 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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### 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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### 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 <...
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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### 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 ...