Questions tagged [equation-solving]
Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
3,674 questions
1
vote
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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$$
Where $a,y,z$ and $a$ are whole real (positive and negative) numbers.
And I want to give ...
0
votes
1answer
48 views
I am trying to solve these Chemotaxis Equations but I can't seem to make it work
I am trying to solve a a pair of coupled partial differential equations but it doesn't seem to work. I am getting the error 'Length of the derivative order is not u1[t,x]the same as the number of ...
2
votes
0answers
27 views
Reduce returns false on equation solvable by LInearSolve
I was looking for general solutions of an equation I already solved for specific values with LinearSolve, but using Reduce returned False.
Here's the code:
...
1
vote
1answer
68 views
Problem finding constants after using DSolve
I have to solve a relatively simple PDE:
$$\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.
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2
votes
0answers
67 views
How to make GroebnerBasis Work or to speed NSolve up
I consider a set of three polynomials of two variables
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4
votes
1answer
834 views
Why does Solve lock up when trying to solve the quadratic equation with large integers?
Why does Solve lock up when trying to solve the equation
...
0
votes
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
vote
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
votes
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
vote
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
votes
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
votes
2answers
106 views
Why does this system of equation not have a solution?
The following set of equations leads to a solution:
...
2
votes
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
votes
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 .
...
