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

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5
votes
0answers
115 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
339 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
58 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
64 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
103 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
202 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
306 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
118 views

Solve Differential Equations with Boundary Condition at Variable Point

I have a set of differential equations: ...
7
votes
3answers
383 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 bad,...
0
votes
1answer
57 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; ...
9
votes
2answers
279 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
83 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 for:...
1
vote
2answers
70 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
130 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 ...
5
votes
3answers
230 views

How to get the coordinates of the intersection of two lines from a ListLinePlot?

Suppose I have two curves intersect at some point, how can I read the coordinates from the graph, not read by eye, but find it with more precision by computer. For example, here are two lists created ...
1
vote
1answer
44 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
124 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) x^2\mathrm{...
2
votes
1answer
264 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
197 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
175 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
94 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
71 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
49 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
254 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
554 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
98 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 $\tau=1$ can'...
2
votes
2answers
190 views

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

I'm a beginner in Mathematica. I'm trying to solve : ...
3
votes
2answers
82 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
146 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 $b\,\...
4
votes
2answers
188 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
39 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
61 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
125 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
64 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
177 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
80 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: ...
1
vote
2answers
99 views

Evaluation to true using DSolve - syntax errors?

Probably a stupid question, apologies, but I am getting an annoying error when I try to evaluate the following simple PDE $\frac{\partial C}{\partial t} = d \frac{\partial^2C}{\partial x^2}$ between $...
8
votes
2answers
131 views

Numerical solve question

Why does this work? Solve[5 Tan[t] + 9 == 0 && 0 <= t < 2 Pi , t] {{t -> π - ArcTan[9/5]}, {t -> 2 π - ArcTan[9/5]}} But this doesn't. <...
3
votes
2answers
194 views

How do I solve for a variable inside a sum but independent of the summation index?

How would I go about solving the following for c? Solve[0 == Sum[(t[i]*m[i] - c*t[i]^2)/s[i]^2, {i, 1, n}], c, Reals] I get ...
0
votes
1answer
77 views

Reducing solutions of Sin[2t] Sin[t] == Cos[t] to a simpler form [closed]

I evaluated Solve[Sin[2 t] Sin[t] == Cos[t] && 0 <= t < 2 Pi, t] And got these results. ...
3
votes
0answers
96 views

Extending Bresenham's algorithm for subpixel rendering

Original Bresenham's line drawing algorithm it limited to drawing lines between two integer pixel positions and does not allow subpixel rendering. However with my reformulation of this algorithm as a ...
0
votes
1answer
101 views

Solve equation with sum in it

Have trouble to solve this equation. Anybody knows where're the problems? ...
0
votes
2answers
178 views

Bifurcation diagram for 1D ising model

I'm new in Mathematica, I want to plot a bifurcation diagram for a complicated Ising system with dynamics that I'm working on, but to get familiar with how to perform it on Mathematica I wish to start ...
0
votes
1answer
32 views

$Failed when naming the variable x [closed]

Total beginner here, the problem goes away when renaming x into other letters. Below is the code ...