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Questions tagged [equation-solving]

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

1
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1answer
46 views

System of coupled differential equations

I am trying to solve the following system of equations, but I get as the output the command itself. ...
-1
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1answer
57 views

Liquefying of Nitrogen & Oxygen Gaseous to Liquid Phase. Thermodynamics. How to plot solution? Solved

Process of Liquefying of air composed of 79% Nitrogen & 21% Oxygen from Gaseous to Liquid Phases as Follows: 1) When Temperature is higher than T>83 k they both are gas. 2) at T=83 k and less ...
2
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0answers
23 views

Convincing Reduce[] to work

The following should return True: Reduce[ForAll[{t, x}, x > 0, Exists[y, x^t == y]],Reals] but ...
0
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0answers
28 views

Having difficulties using results returned by Solve

I'm new to Mathematica, and I am still having some issues figuring out the general syntax. I've got to use Mathematica, as my research requires a powerful symbolic math program. I'm having trouble ...
0
votes
1answer
43 views

Using constraints when solving a trigometric equation

I'm trying to learn how to add constraints/assumptions to equations when using Solve, sp as to avoid multi-valued solutions. For example, I'm trying to use ...
0
votes
1answer
52 views

How to solve this equation numerically? [on hold]

Two Gaussian functions: f1,f2 of the form f1 = a1*Exp[-t^2/s1^2]. Total area, Atot of (f1+f2) is known. Height of each peak (a1 and a2) is known (experimental ...
3
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2answers
83 views

How to solve these ODEs using NDSolve?

I have six odes and I cannot use DSolve. So I tried NDSolve. But it says there may be some errors.The code is such like this: ...
6
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1answer
124 views

Maxwell construction problem with FindRoot

A Maxwell construction is just an integral of area and then solving for a root to find vapor pressure. This must be exactly the same value as where the Gibbs energy plot crosses at a point. I found ...
0
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1answer
47 views

Solve a complex equation symbolically?

I try to solve this equation symbolically: Solve[A*s - b*Log[Sqrt[(d - e*s)^2 + 1] + d - e*s] - x + b*c == 0, s] (yes: ^2 = cntrl-6) But M. (trial version) is ...
0
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1answer
59 views

Dynamically evaluating integrals where the limits of integration must be found with FindRoot

I've the following problem: I need to use Manipluate to scroll over different values for $\text{R}$ ($0<\text{Rb}\le10^5$) and plotting for values of $0<\text{c}<10$. So, I have the ...
0
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0answers
103 views
+150

Solving for coefficients of a polynomial ansatz in a rational function

Firstly, I apologise for the numerical messiness, and for the extended length of this question. If this is successful, this is the last question I will need to ask for a long time. I start with a ...
0
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1answer
63 views

Solve nonlinear system with eight variables

Please I realy need Help We consider the three functions H1=4(x+b1 y)^2+8(c1x-d1 y)+e1^2 y^2, with e1>0 H2=4(x+b2 y)^2+8(c2 x-d2 y)+e2^2 y^2, with e2>0 H3=4(x+b3 y)^2+8(c3 x-d3 y)+e3^2 y^2, with ...
1
vote
1answer
54 views

Finding all positive roots of a transcendental equation [duplicate]

I need to find all positive roots of the following transcendental equation 2*cot(x) = 6.4*x-0.1563/x I know that the roots can be visualised as the intersecting ...
0
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0answers
50 views

Sum of Roots of a Cotangent equation

I want to reproduce a model calculation, which seemed straight forward, but one piece is puzzling. The (quite simplified) function is: ...
0
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0answers
39 views

High degree equation solving [duplicate]

I want to solve the following high-degree equation eq1 = (2*t^3*θ^2)/(1 + t*θ*(2 + 3*t*θ)) + (1 + 3*t^2*θ^2)/(1 + t*θ*(2 + t*θ*(7 + 2*t*θ))) == 0 and the ...
0
votes
2answers
60 views

A system of non-linear equations with no real-valued solution

I am trying to solve the following system of non-linear equations with mathematica. I have tried NSolve, Solve and findRoot. All the solutions they return are complex-valued. I am still a little ...
0
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0answers
45 views

DSolve leads to an equation that is different from paper solution

I'm following the method in the two images in an attempt to obtain a value for $\beta$. I know that there's a mistake in (4.36) from here so I used Mathematica's solution to continue the solution. I ...
2
votes
2answers
58 views

Extra constant in solution of ODE using DSolve [on hold]

A paper that I have states that the solution of the ODE $$-\frac{\left(\frac{\pi k}{a}\right)^2 Y(y)}{G_y}+\frac{Y''(y)}{G_x}+\frac{8 \theta }{\pi k}=0$$ is $$Y=A\sinh\left(\frac{k\pi\mu}{a}y\right)+...
0
votes
0answers
46 views

Looking for integer solutions to an equation [closed]

I want to have code, where I can solve the following equation for whole numbers: $$x^3+y^3+z^3=33\tag1$$ Where $a,y,z$ and $a$ are whole real (positive and negative) numbers. And I want to give ...
0
votes
1answer
48 views

I am trying to solve these Chemotaxis Equations but I can't seem to make it work

I am trying to solve a a pair of coupled partial differential equations but it doesn't seem to work. I am getting the error 'Length of the derivative order is not u1[t,x]the same as the number of ...
2
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0answers
27 views

Reduce returns false on equation solvable by LInearSolve

I was looking for general solutions of an equation I already solved for specific values with LinearSolve, but using Reduce returned False. Here's the code: ...
1
vote
1answer
68 views

Problem finding constants after using DSolve

I have to solve a relatively simple PDE: $$\frac{\phi_{xx}(x,y)}{A}+\frac{\phi_{yy}(x,y)}{B}=-2 \theta$$ where $A$, $B$, and $\theta$ are constants. The code that I used was ...
2
votes
1answer
40 views

Plotting numerical solutions (multi solutions)

I am trying to plot the solutions of this equation. ...
2
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0answers
67 views

How to make GroebnerBasis Work or to speed NSolve up

I consider a set of three polynomials of two variables ...
4
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1answer
834 views
0
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2answers
96 views

Solve only finds the trivial solution

I'm pretty sure eqn1 and eqn2 both have non-trivial solutions. They are a very similar set of simultaneous equations generated ...
1
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1answer
75 views

Solving recursive equations with RSolve, with constraint and subscripts

I'm trying to solve this set of equations in generality, where $n$ can vary. $\begin{align*} P_{1}&=1-\sum_{i=2}^{n}P_{i}\\ P_{i}&=\frac{c_{i-1}P_{i-1}}{c_{i}+\mu_{i}}, \quad i=2,\dots,n-1\\ ...
4
votes
2answers
182 views

Find maximum of the output from reduce

I am trying to reduce a function in two variables($n_1$ and $n_2$) whose domain is the set of Integers. I get a long list of pairs of values for these two variables(instead of a range). This could be ...
0
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0answers
69 views

Numerical Solution of giant Analytic DE

I have a little bit of a problem regarding numerical solutions. I have a system of two entirely symbolic differential equations of two functions, F[r] and K[r]. One of them is fairly simple, but the ...
1
vote
1answer
29 views

Find coefficient in a linear combination

It's a very simple problem, but I don't find the way to solve it with Mathematica. let's say $A=a+b$, $B=3a$, $G=b$. I want to find at least one (if any) solution to $x A+ y B=G$ for $x,y$. I tried ...
1
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0answers
62 views

Connection between a symbol and its subscript form?

I have read all about subscript forms and that they are DownValues of Subscript[]. I still do not understand the following: ...
0
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0answers
74 views

Why does Solve not find solutions in terms of radicals?

Let's consider the following system of polynomial equations. The s and the capital S are two different variables (I know the ...
-1
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2answers
106 views

Why does this system of equation not have a solution?

The following set of equations leads to a solution: ...
2
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3answers
53 views

Plotting Solve output automatically

I am trying to solve a characteristic polynomial and plotting its output. The problem is that I do not know how to take the output automatically. My current code is ...
0
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0answers
56 views

Calculating forces on a truss

I need to find certain forces of the truss shown above, and I am asked to calculate the forces with a matrix. The given values are ...
2
votes
0answers
67 views

How to prove subspaces of function spaces?

In teaching Linear Algebra, I would like to prove or disprove whether a nonempty subset of a vector space, is a subspace. For this, I would show that the subset is closed under both addition and ...
1
vote
2answers
66 views

Constrained summation problem [closed]

Here is a problem from Brilliant.org: where each symbol has a fixed numerical value and the sums in each row and column are given (except one). The task is to find the sum in the first row. Why ...
6
votes
2answers
143 views

Equation with several exponents

Is there a way to get the result for this value of x? x^x^(x^(1/6)/6)==Sqrt[2^9]^(2*Sqrt[2])^(2/3+2*Sqrt[2]) I've tried Solve,...
0
votes
1answer
59 views

Don't understand why Solve fails to find solution for my system of equations [closed]

I have one set of equations which Solve can handle, but when I give Solve second set (which I think is very similar to the first)...
2
votes
3answers
149 views

FrobeniusSolve with solutions only being 0 or 1 being acceptable

I want an EFFICIENT way of solving the Frobenius Equation a1 n1 + a2 n2 + a3 n3 + ... + aK nK = U where n1, n2, ..., nK are restricted to be either 0 or 1. I ...
3
votes
1answer
157 views

One term in non-linear equations prevents NDSolve to work

I am currently working on the stratification of the core of the planet Mercury, meaning the formation of a conductive layer at the top of the convective core, with a moving interface between both ...
2
votes
1answer
43 views

Another using Solve output for further calculations

I probably missed a question already posted as this topic seems common, but I looked at several, e.g. Using result of Solve in further calculations and am a little stuck. I didn't understand the use ...
9
votes
3answers
306 views

Solving an integro-differential equation with Mathematica

I try to solve a nonlinear integro-differential equation with this code. Here i used a periodic condition. ...
0
votes
2answers
79 views

Find $\text{k}$ such that $:$ $\text{discriminant}= 0$ [closed]

I tried to find $\text{k}$ such that $:$ $$\text{discriminant}\left [ \text{discriminant}\left [ z^{\,2}\left ( z^{\,2}- 1 \right )^{\,2}\left ( z^{\,2}+ 1 \right )+ \left ( y^{\,2}- z^{\,2} \...
0
votes
1answer
58 views

Finding Steady States that Meet Additional Constraints

I've written a function that returns the steady state given a regular, column-stochastic matrix. I want to use it to solve a larger problem, finding steady states that satisfy certain conditions. The ...
3
votes
4answers
161 views

How do I declare a countably infinite list of variables as being integers?

I want to do this, Solve[ { n1 + n2 + n3 + .... = 10, n1 + 2 n2 + 3 n3 + .... = 100}, {n1,n2,n3,....}, Assumptions -> {n1,n2,n3,.... are Integers >=0} ] ...
1
vote
1answer
67 views

Solve can't find a solution for a transcendental equation

I'm trying to solve a system of equations. The problem I'm encountering is that one equation is transcendental and Solve is unable to find a solution for it, so can'...
1
vote
1answer
71 views

How to use Solve properly

I'm attempting to solve the following system of equations for k and $\kappa$ $$\mu\epsilon\omega^2=k^2-\kappa^2$$ $$\mu\sigma\omega=2k\kappa$$ but when I type into Mathematica ...
0
votes
1answer
78 views

Interval determination with mathematica [closed]

I am given the solution y=yo/(1-yo x^2). If yo>0, the solution is valid only on ( -1/sqrt(yo), 1/sqrt(yo) ). How is this determined? I need a proof like answer and I need it programmed in ...
0
votes
2answers
48 views

Question about equation solving and its solution

I want to find alpha which is the root of the following . ...