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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Maximizing a function that is only defined numerically

I have a function of multiple variables that is only defined numerically. I am trying to maximize the function and find the critical points as fucntions of two parameters p and s using FindRoot but I ...
jcl's user avatar
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4 votes
0 answers
43 views

Speed up this computation involving NSolve many times?

Can you think of a way of speeding up this computation ? I don't. ...
anderstood's user avatar
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1 answer
43 views

Plotting an integral with solving for a specific constant [closed]

Given an Integral I(t) which is a function of a constant tc, this constant is determined with the condition I(tc)=0, how can I add this condition?
Med Ch's user avatar
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1 vote
1 answer
59 views

Strange behavior of GroebnerBasis

Recently I tried to solve a multivariate quadratic equation over the reals, but with a parameter value. Since that took too long, I decided to try GroebnerBasis, ...
AYun's user avatar
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0 answers
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How do I find roots of a third degree polynomial? [closed]

expr = G^2 X^3 - 2 Δ G X^2 + Δ^2 X + ((ℏ *G*η* k*Subscript[E, l]^2)/(m*Subscript[Ω, m]^2)) == 0
abdul wahab's user avatar
1 vote
2 answers
70 views

How to modify the order of symbols to make the result more logical [closed]

Simplify[(1 - a) (1 - b)] (-1 + a) (-1 + b) How to modify the order of symbols to make the result more logical. (1-a)(1-b)
Chin Ching CHAN's user avatar
0 votes
2 answers
144 views

Solution of a sixth degree polynomial

I want to get the solution to a 6th degree polynomial in a certain range. I have the following code ...
Geigercounter's user avatar
2 votes
2 answers
105 views

FindRoot with input as a list

I have three equations: eq1, eq2, eq3 with variables a,b,d,k. I wish to find the roots of these equations by assuming ...
Math_student's user avatar
-1 votes
1 answer
77 views

Adding Points on an Elliptic Curve

How do I do this in Mathematica? The curve given by the equation $y^2 = x^3 + 29x + 7$ defined over the integers modulo $10007$ Adding the first pair of points $P = (3737, 4549)$ and $Q = (8286, 6097)$...
Bob's user avatar
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2 votes
3 answers
240 views

Getting all solutions to an equation on condition the variables are either 0 or 1

Given a list of 3-bit binary lists b={{0,0,0},{0,0,1},{0,1,0},{0,1,1},{1,0,0},{1,0,1},{1,1,0},{1,1,1}}; I would like to have all possible solutions to ...
Phillip Dukes's user avatar
1 vote
1 answer
140 views

Numerical solving diffusion equation in spherical coordinates

Mathematica nicely solves Poisson's equation in spherical coordinates as ...
Rodion Stepanov's user avatar
1 vote
1 answer
53 views

First order differential equation with two conditions

I want to produce all possible solutions for this equation: ...
Mathecis's user avatar
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1 vote
1 answer
62 views

Problems with Solve. Only works for specific parameters. Solve function do not "start"

I have the following problem I want to solve the following equalities. My used code: ...
Tremonia's user avatar
2 votes
1 answer
141 views

How to solve this integral equation numerically?

I am encountering difficulties while trying to numerically solve an equation in Mathematica that involves an unknown function and an integral. Specifically, the equation takes the form of \begin{...
dcmpsr's user avatar
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2 votes
2 answers
77 views

Selecting Solve results according to conditions

When using the Solve function I get four possible answers. How can I automatically get the option in which x and y are positive? Where to insert the conditions x>=0 and y>=0? ...
Vladimir's user avatar
1 vote
2 answers
150 views

How can I choose the integer numbers a, b, c, d, t so that the equation $\sqrt{a x^2+b x+c}=d x+t$ has two integer solutions?

The equation $\sqrt{x^2+36 x+180}=2 x+15$ have two integer solutions are $x = -5$ and $x = -3$. How can I choose the integer numbers $a, b, c, d, t$ so that the equation $\sqrt{a x^2 + b x + c} = d x +...
Rosa_2023's user avatar
1 vote
0 answers
59 views

Why this Solve cannot be solved [duplicate]

Solve[Sum[p*a[i], {i, 1, n}] == 0, p, Reals] Solve[p*Sum[a[i], {i, 1, n}] == 0, p, Reals] The first line of code cannot be solved, but when the variable ...
Yilin Cheng's user avatar
3 votes
2 answers
98 views

Solving A System of Two Implicit Equations

I am solving a system of 6 equations, and I am interested to know the solution for different rhoBar values. Here is the input parameters: ...
joe's user avatar
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2 answers
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Can a redundant condition be removed from a solution?

A solution to this equation: Solve[{(p-x)^2 + (q-y)^2==d, p/q==t}, {p,q}, Reals] has this repetitive condition: $\displaystyle\quad d > \frac{x^2 - 2txy+t^2y^2}{...
scriptfoo's user avatar
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0 votes
1 answer
51 views

How can i create an equation with a sum? [closed]

I have a list of $p_i$ and the condition that $\sum_{i=0}^{i=69} p_i = 1 $ I also have a list of 69 other different equations. I want to use NSolve to solve for the ...
100xln2's user avatar
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1 vote
1 answer
99 views

How to find the variable $k$ which minimizes the function $\Omega^2$?

$$\Omega^2(k) = 4(\sum\limits_{m=1}^{\infty}\frac{1-\cos(km)}{m^{1+\alpha}})(\sum\limits_{m=1}^{\infty}\frac{1-\cos(km)}{m^{1+\alpha}} - A^2)$$ Let $A = 1$ and $\alpha = 1$ and write $w(k) := \sum\...
KZ-Spectra's user avatar
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0 answers
50 views

Get curve equation from parametrization

I am quite new to Mathematica and I have been wondering how to do this one very specific thing. I have two functions $x(t)$ and $y(t)$ that are the parametrization of a curve, how would I get the ...
Memat's user avatar
  • 101
0 votes
2 answers
82 views

`Reduce` is running forever

I'm trying to solve the last inequality in Reduce in the code below in terms of rmax under the parameter conditions included in <...
ppp's user avatar
  • 979
0 votes
0 answers
58 views

How to speed up maximization of the Solve output?

I am trying to maximize the solution of the system of algebraic equations for different values of parameters. The problem is related to the absorbing times in Markov chains. Here is the code ...
San's user avatar
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3 votes
1 answer
143 views

Cannot solve this polynomial equation

I'm trying to solve the following polynomial equation for $x$: $$ (qx)^\alpha (1-qx)^{1-\alpha} = [(1-q)x]^\beta [1-(1-q)x]^{1-\beta} $$ where $\alpha, \beta, q, x$ are all strictly between 0 and 1. ...
raving-bandit's user avatar
2 votes
3 answers
129 views

Multiple solutions from NSolve

I have a list of polynomial equations which I can solve using NSolve. However, it gives me a large number of similar solutions. The solutions are largely identical ...
Hugh's user avatar
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1 vote
1 answer
63 views

Solving a non-algebraic equation at the symbolic level [closed]

Versions 10, 11, 12, 13.0.0.0 and 13.2.0.0 solves the following system of equations ...
Vaclav Kotesovec's user avatar
1 vote
1 answer
60 views

Newton Raphson apply to Van der Waal Equation

I need assistance with this problem. I have two functions, where f1 corresponds to the dimensionless van der Waals equation of state, and function 2 corresponds to the dimensionless chemical potential ...
Larissa Santos's user avatar
1 vote
1 answer
62 views

Find an instance satisfying equation

I have the following equation with two variables xi and nu. ...
Dotman's user avatar
  • 414
0 votes
1 answer
30 views

Solving Nonlinear Algebraic Equation

What is wrong with the code below? Mathematica is taking a long time trying to solve it. ...
Jose Lockhart's user avatar
0 votes
1 answer
71 views

Solving inequality with `Reduce` doesn't work

I'm trying to solve an inequality in terms of one variable under some conditions for parameter. Here is the code. ...
ppp's user avatar
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0 votes
1 answer
108 views

Newton-Raphson Method Errors

I need assistance with this problem. I have two functions, where f1 corresponds to the dimensionless van der Waals equation of state, and function 2 corresponds to the dimensionless chemical potential ...
Larissa Santos's user avatar
2 votes
2 answers
181 views

Real zeros of complex function

I must find the zeros of a complex function $\xi$ that depends upon two real variables $B$ and $k$. The function is obtained by evaluating the determinant of the identity matrix of dimension $2n$ ...
Dario Bercioux's user avatar
1 vote
0 answers
69 views

How to solve differential equations in just in reals? [closed]

I am working on a variation problem: My goal is to find the curve that connects a point $(x_1, y_1)$ to another point $(x_2, y_2)$. When this curve is revolved around the x-axis, it should generate a ...
Zhang Xuan's user avatar
0 votes
2 answers
120 views

Limit the number of the results returned by Solve to some specific number

I have this Solve: ...
Dani's user avatar
  • 3
1 vote
2 answers
111 views

How to solve this integro-differential equation in Mathematica?

I am a new user of Mathematica, and I am trying to figure out how to solve the following integro-differential equation in Mathematica: $\frac{\partial c(x,t)}{\partial t} = -2 \mu x c(x,t) + 4 \mu \...
Matt's user avatar
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0 votes
1 answer
126 views

Solve[] isn't producing a correct result

I want to find the exact algebraic roots of the following function in terms of Z, P, Q, <...
Lawton's user avatar
  • 103
0 votes
1 answer
56 views

Is it possible to get rid of the square root in the solutions of the following symbolic quadratic equation?

I have a quadratic equation, which I want to solve, but don't want the square root to appear within the solutions. I tried converting the discriminant into a quadratic form but failed, not sure if ...
larry's user avatar
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0 votes
0 answers
50 views

How does Mathematica select principal roots of complex numbers?

When I do I^(1/3) I get Out[]:= (-1)^(1/6) which is one of the solutions of $z^3=i$. There are two more solutions which are ...
sam wolfe's user avatar
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3 votes
1 answer
141 views

Solving system of first order PDEs

I am trying to solve the 1st order PDE system \begin{align} \xi_u^2+\eta_u^2&= \left(1+\frac{\xi^2+\eta^2}{4} \right)^2\\ \xi_v^2+\eta_v^2&=\left(1+\frac{\xi^2+\eta^2}{4} \right)^2 \end{align} ...
Daniel Castro's user avatar
-1 votes
1 answer
45 views

How to convert the equation into this two forms?

The equation is: x0^2/a^2 - y0^2/b^2 == 1 How to convert to this two forms: b^2 x0^2 - a^2 y0^2 -> a^2 b^2 and ...
csn899's user avatar
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1 vote
0 answers
86 views

Attempt to find a solution (out of potentially many) to a system of equations with FindInstance runs forever or crashes

I have a system of equations that in principle should have a solution (I would think not a unique one), which I want to solve. I am not interested in all solutions; I just want to locate one, assuming ...
AG1123's user avatar
  • 561
1 vote
0 answers
58 views

Computing Displacement Potential functions

I am new to Mathematica. I am trying to compute the displacement Potential functions. My code is as follows. ...
S. Pant's user avatar
  • 11
0 votes
2 answers
56 views

How to interpret the solution and how to work with it further?

Please help me understand the solution to the following problem: ...
Vladimir's user avatar
1 vote
1 answer
77 views

Minimization of an implicitly specified function

exp - an experimental data, where expT - temperature, expChi - magnetic susceptibility I ...
Mam Mam's user avatar
  • 1,753
1 vote
1 answer
212 views

How to simplify? [closed]

The original formula is: Abs[(a b)/x0]/(2 Sqrt[1 + y0^2/x0^2]) How do you convert operations to get this result? ...
csn899's user avatar
  • 2,879
0 votes
1 answer
85 views

How can the process of hyperbola problems achieve the desired results?

As shown in the picture above, in the hyperbola x^2/a^2-y^2/b^2==1, point P is any point on the hyperbola, through the point P respectively do two asymptotes of the hyperbola parallel line PA, PB. The ...
csn899's user avatar
  • 2,879
0 votes
3 answers
103 views

Calculate Bernoulli numbers ( with a twist) [closed]

Mathematica has an inbuilt function BernoulliB that calculates $B_n$ for which, $$\frac{t} {\left(e^t-1\right)}=\sum_{n=0}^{\infty} \frac{B_n}{n !}t^n $$ I need to ...
Dotman's user avatar
  • 414
0 votes
1 answer
49 views

How do I plot a 2D function with an intermediate variable?

I have a function $c\cdot\frac{x^2}{x^2 + 10^{-6.367}*x + 10^{-6.367-10.32}} + x = c\cdot\frac{10^{-6.367-10.32}}{x^2 + 10^{-6.367}*x + 10^{-6.367-10.32}}+\frac{10^{-14}}{x}$, where $0 < x < 10^{...
HasturQ's user avatar
0 votes
1 answer
114 views

Kernel Crash Using Solve

The following code crashes the Kernel with no error message. ...
Just Some Old Man's user avatar

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