Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).

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6
votes
0answers
206 views

Solving a nasty equation

Here's an equation that I need to solve for $t_k$ $$ \theta_0 = \tan^{-1}\left(\frac{2(w_x - m)}{p - g {t_k}^2 - 2 t_k w_y}\right) - {\frac{1} {r}} \left( \left(\frac{m}{t_k}\right)^2 + \left( ...
0
votes
1answer
43 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
0answers
64 views

Speed up the Eliminate

I have problem of eliminating some variables from a set of equations, which contain logarithmic function, in order to obtain a differential equation. These are the parameter and functions in ...
-1
votes
1answer
54 views

Solve Numerical Equation [closed]

I want to find $x\in \ \mathbb{Q} $ such that the first ten digits of $ x \pi $ are 1.234567890. I tried: ...
1
vote
1answer
73 views

Plotting data from a Table in Mathematica

I have been able to solve some differential equations using Tables. The code works fine without errors. However, I am unable to plot the results. Any help would be appreciated. ...
1
vote
3answers
94 views

Find all solutions which satisfy the given conditions

Let $$ m=9n^3+30n^2-9n $$ where $n \in \mathbb{Q^{+}}$ and $m \in \mathbb{Z} $ . Find all solutions which satisfy the given conditions. So I've tried to solve this manually and I was ...
1
vote
1answer
340 views

How to code the following in Mathematica

How do I get the following into Mathematica, solving for a: $$ 0.7 = 1 - \frac{2}{a} \times [ \frac{1}{a} \int_0^a \frac{x}{\exp(x)-1} dx + \frac{a}{6} - 1] $$
4
votes
2answers
1k views

Can mathematica solve this equation?

I have the following Mathematica code to solve an equation coming from isoparameteric finite element for quadratic tetrahedron element. I need to get the iteroplation fast and accurate. I only find ...
1
vote
2answers
216 views

Need help solving a system of two 1st order nonlinear differential equations

The original system of equations reads: $\begin{cases} f'(r) + f(r) \left(a(r) - \frac{1}{r}\right) = 0,\\ f^2(r) + a'(r) + \frac{a(r)}{r} - 1 = 0\,, \end{cases}$ with boundary conditions $f(0) = ...
1
vote
1answer
58 views

Improving strategy to solve this constrained root-finding problem

I am looking for roots of the function eqs defined below. It has $2k$ unknowns and returns a vector of $2k-1$ components. The sole purpose of the following block ...
2
votes
0answers
86 views

Solving this system of nonlinear equations

Edit Interestingly, I realized solving my problem with $2n$ equations appeared to be more efficient than using mathematical results on the solutions to reduce the problem to $n$ equations (the $n$ ...
0
votes
0answers
27 views

Solve involving simple cancellation on both sides fails when there are too many constants

I've been working with a number of equations of the form x = A * B * x ^ C where I need to solve for x--basically, equations ...
0
votes
1answer
76 views

Nonrectangular tensor encountered [closed]

I am trying to solve a system of equations which characteristic matrix: ...
3
votes
1answer
100 views

How do I solve a system of equations for only one variable quickly?

I have four order-2 polynomial equations in four unknowns. Call the unknowns x1,x2,x3,...
0
votes
0answers
40 views

Probleme with Ted Ersek's RootSearch package [duplicate]

The following question is a logical continuation of this one. The Ted Ersek's RootSearch package doesn't work with this code: ...
0
votes
3answers
122 views

Manipulation linear systems of equations

I have the following system of equations: i1 = ix - β*ib; i2 = (β + 1)*ib; i3 = ix + ib; vx = i1*Rc + i3*Rb; v1 = i2*Rϵ + i3*Rb; v1 = -ib*rπ; I tried using: ...
0
votes
0answers
140 views

No solution with DSolve

I have been trying to solve the following system of ODEs: \begin{eqnarray} ...
3
votes
0answers
112 views

Complex boundary conditions and NDEigensystem

I am having difficulties implementing a Neumann value when numerically solving the Navier equation using NDEigensystem. The Navier equation is given by $\nabla^2 \vec u + (p^2 - 1) ...
0
votes
1answer
114 views

Conditions for real roots of a cubic polynomial with complicated, yet constant, parameter values

Can anyone find conditions on the following parameters $\sigma_{\ell}$, $\mu_{\ell}$, $d_{\ell}$ and $\sigma_M$ such that the cubic: $$ (d_{\ell}-d_{\ell}\sigma_M)\ell^3 + ...
1
vote
1answer
81 views

Help with findroot optimization

I'm trying to solve the set of coupled equations $$\frac{-N -2( \lambda + N(\frac{\beta}{\epsilon}-\lambda))\upsilon_l + N ...
4
votes
1answer
112 views

Solving for the roots of a trilinear system of polynomials

I have been trying to solve for the roots of the following system of trilinear polynomials: ...
0
votes
0answers
60 views

Solve a system of first order ODEs with variable coefficients

I am totally new to Mathematica, so sorry if my question could seem stupid. I'm trying to solve this system of ODEs \begin{align*} &S'(a)=-\lambda(a)S(a)+{\tau}R(a)\\ ...
3
votes
2answers
82 views
0
votes
1answer
71 views

Invert and fit implicitly defined curve

I need to fit an implicitly defined curve. I thought I could get some data out of Solve, and then using FindFit. Therefore, I ...
1
vote
2answers
80 views

Solving an equation of one parameter over a range of values of that parameter [closed]

How can I use NSolve the following situation (to rectify a cycloid arc mapping with hashes etc.)? For a specific value on the right-hand side, I use ...
-2
votes
1answer
61 views

How to solve this non-linear equation? [closed]

b=12 a=2.787 solve[b/x-((1-(a*(((b x)/(b+2 x))^(4/3))))^(-2/3))- ((1+(a*(((b x)/(b+2 x))^(4/3))))^(-2/3))==0,x] I gave the above code and the output came ...
1
vote
1answer
48 views

Mathematica cannot find intersection of two functions [closed]

Why mathematica cannot solve this extremely easy equation? [![My functions][1]][1] g[x_] := -x + 2 h[x_] := 3 x f[x_] := -x^2 + 4 http: // ...
2
votes
1answer
75 views

How to put the result of NDSolve in a function?

I have solved an ODE with NDSolve, and put the result in S: S = NDSolve[{y'[x]==(y[x]^4+y[x]+1)^(1/2),y[0]==0}, y, {x, 0, 100}] But i don't want to plot y[x] ...
0
votes
3answers
90 views

Solving cubic equation with unknown coefficients

I am trying to solve a cubic equation with unknown coefficients (p and t), here is the code: ...
6
votes
1answer
2k views

Efficient implementation of cubic equation of state

...In this case the Peng Robinson Equation of State. Equations of state are empirical equations with parameters derived from experimental data. They are used to predict pure component and mixture ...
7
votes
2answers
299 views

How can I find solutions for this equation?

I have a function cxyz[s1, e1, s2, e2], and I want to find at least one set of {s1, e1, s2, e2} for which the function's output ...
0
votes
1answer
71 views

Implementing AiryAiPrimeZero function

There are some functions implemented in the Wolfram Language related to Airy functions. For example, AiryAi, AiryAiZero or ...
1
vote
4answers
144 views

Find zeros of a transcendental function

Mathematica 10 can not give me solution of this equation ...
1
vote
0answers
84 views

Solve works with numbers, but not with free variables [closed]

The following code prints the correct solution for variable a (2.23). But if I comment out the five assignments given at the top, the code fails. When I remove ...
3
votes
2answers
115 views

Plotting solutions of systems in complex plane

I'm interested in plotting solutions of systems of polynomials in the complex plane, in the following way. Let $f_1,\ldots f_s$ be complex polynomials in variables $x_1,\ldots x_n$. I know how to ...
0
votes
1answer
65 views

How to solve a linear system inside Manipulate and use the result for Plot?

I typed a code for showing a plane and a line, and solve a system, but I can´t show the intersection, because I don´t know. Here is a minimal working example for understanding my problem ( the real ...
0
votes
3answers
117 views

Find zeros of function in 2 variables

I have two functions $f(r,\phi)$, and $g(r,\phi)$. What is the best way to find the curve in the plane $(x,y)$ or $(r,\phi)$, over which $f(r,\phi)=g(r,\phi)$? I know how to plot it, using ...
4
votes
3answers
96 views
1
vote
1answer
40 views

FindRoot::Istol error

I recently tried to find a root with FindRoot in Mathematica. I know that the problem has a solution, but when using FindRoot, this error appears : ...
2
votes
0answers
45 views

Why doesn't RSolve work here? [closed]

RSolve[ {θ[n + 1] == θ[n] + 0.25*ϕ[n], ϕ[n + 1] == ϕ[n] - 2.5*Sin[θ[n]], θ[0] == π/2, ϕ[0] == 0}, {θ[n], ϕ[n]}, n] What's wrong with my code? I know ...
1
vote
0answers
59 views

Why FindRoot fail in this case?

I'm trying to solve a set of equations: $$\frac{\epsilon+(k(1-N)+2\beta)\upsilon_l-\epsilon \upsilon_l^2-2\Omega(1-N)\upsilon_l^3}{-\Omega\upsilon_l^4+k\upsilon_l^2-\Omega}=\sum_{j\neq ...
1
vote
1answer
59 views

Assigning solutions to a variable [duplicate]

If I do Solve[x+1==0, x] then I get {{x -> -1}} But I want to assign the solution -1 directly before seeing the result, ...
0
votes
0answers
48 views

FindRoot for vectors

My problem is the following: quad = 26; R is a quad x 3 matrix, lpand ...
5
votes
5answers
139 views

Non-algebraic equation in the set of complex numbers

The following equation in $\mathbb{C}$: $4z^2+8|z|^2-3=0$ is not algebraic and has 4 solutions : $\pm\frac{1}{2}$ and $\pm i\frac{\sqrt{3}}{2}$. The Solve function in Mathematica only returns the 2 ...
1
vote
0answers
70 views

Solving a tensor equation in xTensor [closed]

I want to solve the following equation $\frac{1}{4} R_{ab} g_{cd} - \frac{1}{2} g_{ab} R_{cd} + 4 R_{ab} g^{ef} \nabla_e \nabla_f R_{cd} + 2 g_{ab} R_{cd} g^{ih} g^{ef} \nabla_e \nabla_f R_{ih} = ...
2
votes
0answers
73 views

Solving a non-linear equation in Mathematica with many variables

I have a beautiful equation, where I am trying to compute for R2. I am using Mathematica. So far every single time that I have tried to use Solve[] or Reduce [] the computation takes forever. I hope ...
9
votes
2answers
159 views

Does LinearSolve know that I gave it a Sparse lower triangular matrix?

Let $\mathbf L$ be a nonsingular numeric (non-symbolic) large, lower triangular sparse matrix. Let $\mathbf b$ be an appropriately sized vector. I want to solve $\mathbf L\mathbf x=\mathbf b$. ...
0
votes
2answers
278 views

How to write Newton-Raphson module and return a value?

I am writing a code which solve nonlinear algebraic systems via Newton-Raphson algorithm. I want to make a Newton Module with another file and use the Module in my test file, but i didn't achieve it. ...
2
votes
1answer
33 views

Specifiying values in a system of equations

Suppose I have system of equations, for example Clear[a, b, c] Reduce[{RCI7[{a, b, c}] > 0, RCI7[{b, c, a}] > 0, RCI7[{c, a, b}] > 0}, {a, b, c}] // N ...