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

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5
votes
5answers
160 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 ...
2
votes
0answers
97 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 ...
2
votes
1answer
34 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 ...
0
votes
2answers
53 views

Please, can someone solve this equation [closed]

Solve the equation: e^(at)+e^(a(t-T)) = 2. Please can someone help me to solve this equation. I need a in terms of t, T.
0
votes
1answer
72 views

a question about Nminimize [closed]

I have 10 equations and 10 unknown parameters such as alpha1,alpha2,a1,a3,... which I want to find them by minimizing ...
5
votes
0answers
95 views

Find regions in which the roots of a third degree polynomial are real

I have to find the roots of a third degree polynomial in $\phi$ that depends from 3 parameters, namely $t,s,w\in \mathbb R$. In order to do that I've used the command ...
4
votes
2answers
124 views

Torus-geometry algebraic equations using Nsolve and Reduce

Somehow a set of naive-looking equations cannot be solved by using NSolve. Mathematica returns a message like this: ...
-1
votes
1answer
39 views

Finding the set of solutions of an equation [closed]

I have a very simple problem. I have an equation f[x] == 0, where f[x_] := x^2-4. In output, I want to get the set of ...
1
vote
1answer
41 views

defining output Solve

I'm just starting with Mathematica and I was having a small question: How can you "define" the outcome of a "Solve" in Mathematica? Here is an example from mathematica: ...
5
votes
0answers
110 views

How to find an algebraic representation

I want to find matrix representation of some algebra (Clifford algebra Cl(3,1) in this case). Here is an example, which I would like to get and then extend to higher dimensional matrices. Suppose we ...
7
votes
2answers
323 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 ...
1
vote
1answer
54 views

Problems with solutions obtained from Reduce

I am solving a problem using Reduce, and having a difficulty with understanding the answers I obtained. I was solving ...
1
vote
0answers
62 views

Getting Solve::nsmet error message

I have the following equation: Profit[Fc_] = p (T - Fs - Fc)^(rho*phi) * Fc^phi * Mc^psi - w*Fc and I tried ...
2
votes
1answer
97 views

Reduce not solving linear equation

I have a long equation in 7 variables but the equation is linear (affine) in x. But when I try to solve with Reduce, it keeps running forever. With Solve, I am able to get an answer. Usually I have ...
0
votes
0answers
20 views

Numerical resolution of equation with trigonometric expressions [duplicate]

I have difficulties to solve this equation : NSolve[(x^3 + Sin[x]*Cos[x]) == 0, x] I receive the following error message : This system cannot be solved with ...
5
votes
2answers
191 views

Series solution of the Lane-Emden equation

I have the following problem: I'd like to show how the Lane-Emden equation would look like if someone would solve it as a series. Here's the code: ...
0
votes
1answer
227 views

How could I solve this Reaction-Diffusion PDE using mathematica?

I'm modeling a problem with PDEs, So I gotta solve numerically this Reaction-Diffusion Partial Differential Equation $$ \frac{\partial u(t,x,y)}{\partial t}=D\Big( \frac{\partial^{2}u(t,x,y) ...
3
votes
1answer
114 views

Solve Differential Equations with Boundary Condition at Variable Point

I have a set of differential equations: ...
7
votes
3answers
373 views

Can't figure out how to plot this function

I've got a real nasty function that I can't figure out how to plot. The function is $\qquad f(k) = \pm\sqrt{1+4\cos^{2}(k/2)+4\cos(k/2)\cos(p)}$ from $k=-\pi$ to $k=\pi$, which doesn't look so ...
0
votes
1answer
48 views

Constraints on Solve results

I'd like to filter the results of a solve giving inequality conditions: let's say I have Solve[f[x]==g[y],y] since i want y as function of x, but I want only the ...
4
votes
1answer
128 views

Solving a linear equation in an abstract vector space

I have five abstract vectors a1,a2,a3,a4 and a5 that yield four other objects through abstract addition w1 = a1 + a2; w2 = a2 + a3; w3 = a3 + a4; w4 = a4 + a5; ...
8
votes
2answers
235 views

How can I get the solutions of $x^n-x-t=0$ in hypergeometric form?

$x^3-x-t=0$ has three roots that can be expressed in hypergeometric form, for example $$x_1=-1-\frac{t}{2}{_2F_1\left(\frac{1}{3},\frac{2}{3};\frac{3}{2};\frac{27t^2}{4} \right)}+\frac{3t^2}{8} ...
3
votes
0answers
75 views

Equilibrium solution to system of 4 ODEs with 6 parameters [closed]

I have the following system of 4 ODEs of 4 state variables $(M_{U},M_{R},F_{N},F_{M})$ and 6 parameters $(\alpha,b,\gamma,\mu_{M},\delta,\mu_{F})$ that I am trying to find the equilibrium solution ...
1
vote
2answers
68 views

Solving for intervals without using NumberLinePlot

I've been struggling to find a way to find an interval solution to an equation/inequality. I know mathematica can do this since for example, ...
1
vote
1answer
50 views

Calculate for k? [closed]

The mathematical question is as follows: Calculate the value of k for which 2x^2 + 4x - k = 0 has equal roots. My working solves it to equal -2, but if we then put this back into the formula ...
1
vote
1answer
128 views

How to find and express all polynomial roots with greatest precision?

I've already plowed through the documentation and a bunch of other Questions on this, but I've only found partial or tangentially related answers. I need numerical results for all of the complex ...
1
vote
1answer
42 views

System of equations from coefficients of series

I have two functions $F_1(a,b,x)$ and $F_2(a,b,x)$ I expand these functions about the point $x=0$ Series[F1,{x,0,2}] Series[F2,{x,0,2}] the coefficients are ...
2
votes
1answer
110 views

How to plot a figure according to two equations?

There are two equations like this: $a=f(x,y)$ and $z=g(x,y)$, where $a$ is a constant. In principle, one can solve $a=f(x,y)$ for $y$ as $y=k(x)$ and substitute it into the second equation to obtain ...
0
votes
1answer
47 views

Presenting the solution of an equation with the form of x=

In Maple you can use {} inside the command in order to present the evaluation as x=... For instance, the command ...
3
votes
1answer
120 views

Solving an equation containing an integral in the unknowns

I have an equation of $x$ and $y$, which reads $$ -\alpha^2+\frac{2}{3} \alpha^3+y^2-\frac{2}{3}y^3+x^3f(\frac{y}{x})=0, $$ where $\alpha$ is positive parameter and $f(x)=\int (1-\tanh x) ...
2
votes
1answer
212 views

Constant Heat Flux Boundary Condition for the Differential Heat Equation

I am attempting to solve the transient heat equation for a very simple geometry and I am getting a junk solution. I have identified two distinct regions (wall and super-heated fluid layer) with their ...
3
votes
3answers
183 views

FindFit with a sophisticated function (integral)

I am trying to find a fit to the distribution function (empiricial data) in terms of a function which is itself an integral of a product of two simpler functions (two polynomials), that is the model. ...
3
votes
0answers
170 views

solve tricky nonlinear ODE on a grid

I've been working on the same question for a while now and would appreciate any advice on what I'm doing wrong or any direction on how to actually solve the problem. :) On xzczd's advice, I retried ...
3
votes
1answer
90 views

Speeding up constrained optimization problem solving

I have a problem on my homework with Lagrangian multipliers that Mathematica has now been bashing at fruitlessly for 10 minutes. I'm not sure whether I did something horribly wrong codewise, but it's ...
1
vote
1answer
68 views

Adding algebraic functions to NDSolve

I want to define an integral function which depends on a system of ODE and is also used to NDSolve the ODEs. ...
1
vote
1answer
48 views

Manipulate - strange behaviour with NSolve (I suppose)

I have written the following code for a mechanical calculation. The calculation works, but as soon as I try to use Manipulate(needed to generate a .cdf after all), ...
5
votes
4answers
249 views

Finding $y$ coordinates for $\sin(x+y)=x^2+y^2$

How can I find the $y$ coordinates of the equation $\sin(x+y)=x^2+y^2$ when $x=0.5$? I've tried NSolve[Sin[x + y] = x^2 + y^2 /. x -> 0.5, y]
1
vote
1answer
396 views

Why is my expression not a quantified system of equations? [closed]

Who can help me to understand why my code is wrong? It is giving me a message saying "is not a quantified system of equations and inequalities"?
1
vote
1answer
96 views

How to increase the precision to get the correct roots at the boundaries?

I want to solve an equation and Plot a graph of $\delta(\tau)$, where $0<\tau,\delta<1$. In principal $\delta(0)=1,\delta(1)=0$. However, when I solve the equation, the points near $\tau=1$ ...
2
votes
2answers
169 views

Solving two non-linear equations with two unknowns [duplicate]

I'm a beginner in Mathematica. I'm trying to solve : ...
3
votes
2answers
75 views

FindRoot, How to Return Null After x Number of Iterations

I am using FindRoot to find the root of a function, say f(x), and going through a loop for different values of ...
2
votes
0answers
133 views

How to solve an equation where the unknown variable is inside the integration [closed]

I have an equation: $$ \frac{1}{g}=\int_0^{\frac{1}{\delta}\sinh \frac{1}{g}} \frac{\tanh\left(0.882\, b\,\delta\sqrt{1+z^2}\right)}{\sqrt{1+z^2}}\mathrm{d}z $$ I want to obtain the relation ...
4
votes
2answers
186 views

How to solve a linear system by LinearSolve when the variables are duplicate?

Given that I have a set of equations about varible $x_0,x_1,\cdots,x_n$, which own the following style: $ \left( \begin{array}{cccccccc} \frac{1}{6} & \frac{2}{3} & \frac{1}{6} & 0 & ...
1
vote
0answers
36 views

Assign the results from a Solve to variable [closed]

I am a new user. I know, that my question was already asked billion times before, for example here, but I still cannot adopt these answers to my problem. In my problem I am solving the equation and a ...
2
votes
1answer
58 views

Newbie Issues with Solving & Plotting a System of equations

I'm having some problems with my mathematica code, I think I'm overlooking something simple. I get valid solutions for u0 thru u4, but it doesnt generate any plot at all. Also, I'd really like to plot ...
0
votes
0answers
120 views

Solving in Mathematica

I am trying to solve system of equations and inequalities in Mathematica. I am having the doubt that how much of preliminary processing should I do before solving. For example, consider a system of ...
2
votes
0answers
61 views

NIntegrate over statistical variables with parameter

Essentially, what I am trying to do is the following: Integrate a function which contains the parameter k ...
9
votes
2answers
168 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 $\mathbf L\mathbf x=\mathbf b$. ...
2
votes
2answers
76 views

Solving a system of vector equations

I had a problem where I had to solve a series of equations where some of the variables can take multiple value such as shown below ...
1
vote
1answer
90 views

Find Values of a and b for a Limit

I am having trouble finding the values of a and b for which $\lim \limits_{x \to 0}$ $(\frac{\sin (ax) + bx)} {(x^3)}) = -32/3 $. In Mathematica I have entered: ...