Questions tagged [equation-solving]
Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
4,782
questions
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15 views
NDSolve is finding a stiff system very quickly trying to solve a large set of differential equations
I'm a physics PhD student solving lubrication equations (non-linear PDEs) related to the evaporation of binary droplets in a cylindrical pixel in order to simulate the shape evolution. So I split the ...
0
votes
0answers
80 views
Three coupled PDEs to be solved semi-analytically/analytically
I have been trying to solve the following three coupled PDEs where the final objective is to find the distributions $\theta_h, \theta_c$ and $\theta_w$:
$x\in[0,1]$ and $y\in[0,1]$
$$\frac{\partial \...
0
votes
0answers
39 views
Do these solutions actually amount to a solution over the Reals and not over the Complexes as Mathematica says?
The following program outputs approximations to ZetaZero[1] and ZetaZero[-1]:
...
1
vote
5answers
82 views
How to prove the inequality $abc(a+b+c)^2≤(a^3+b^3+c^3)(ab+bc+ca)$? [closed]
I need to prove something like that:
For a,b,c>0 prove:
$abc(a+b+c)^2≤(a^3+b^3+c^3)(ab+bc+ca)$.
I know that $3abc≤(a^3+b^3+c^3)$, but then I derived $3(ab+bc+ca) ≤ (a+b+c)^2$, I can't move on.
Can ...
0
votes
0answers
31 views
Problem with plotting ParametricNDSolveValue
I have a problem when using ParametricNDSolveValue. I am trying to solve the following equation, where R is the parameter:
dvdt = (R^2 * L[t])/ 4 * M * c * r
where
...
9
votes
6answers
992 views
Tower of Pisa function
I'm trying to construct a 'smooth' function $f : \mathbb{R}^2 \longrightarrow [0,1]$ such that all level sets $$\{ x | f(x)=y\}$$ are circles in a way that $f$ looks like the 'Leaning Tower of Pisa'.
...
0
votes
1answer
35 views
Having problem in solving 11x11 symmetric matrix in mathematica
I am solving an 11x11 matrix in Mathematica. I am facing problem when I try to find the determinant or eigenvalues of this matrix. The error generated shows that the matrix is not square therefore it ...
2
votes
2answers
52 views
1
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0answers
51 views
is the Fox-Wright Psi solution of the trinomial equation implemented in mathematica?
According to (13.4) in Belkic: the trinomial roots, their powers and logarithms from
the Lambert series, Bell polynomials and Fox–Wright function
https://d-nb.info/1176090631/34
the solution of
...
1
vote
1answer
58 views
5
votes
2answers
173 views
Solve for parameters so that a relation is always satisfied
Let's say I have a function parameterized by a number of variables. As a simple example
$$F(x,y) = ax^2 +by^2-cxy+1$$
I want to find some set of values (doesn't really matter what they are) for the ...
0
votes
1answer
38 views
How do I find the solution of a system of Diophantine equations in two variables? [closed]
If the first equation is 2x+y=152, and the second is x+2y=100, and it is a fact that both variables are whole numbers and x is larger than y, what is the value of x?
0
votes
1answer
36 views
Invertion of an equation involving an integral
I am trying to solve the following equation numerically for $\mu$, but I'd like to keep $T$ and $n_e$ as parameters for easier plots. $$ n_e = \frac{1}{\pi^2}\int_0^\infty dp\, p^2\frac{\sinh \left(\...
-1
votes
1answer
33 views
How to make sure the answer is limited to Positive Reals?
As the title described, there is code:
...
0
votes
0answers
41 views
Solving quadratic eqaution with many parameters [closed]
It seems like Mathematica or my PC has problems to handle long equations:
...
5
votes
0answers
132 views
Incorrect result by DSolve
For real $x$ consider the trivial equation
$$|y'(x)|=-|x|.$$
Since the left side is always positive and the right always negative, there is no solution.
Let's try
...
0
votes
0answers
37 views
Solve a linear system using the substitution method [closed]
I know that, for the substitution method, I have to isolate the first variable, plug the equation for that variable into the other equations, simplify the new equations, isolate the second variable, ...
0
votes
1answer
45 views
NSolve with Bessel and Hankel functions
I have a complicated function that I would like to solve for the roots. The function comprises Bessel and Hankel functions:
...
0
votes
1answer
70 views
Getting $RecursionLimit errors with FindRoot [closed]
The first time I ran the cells the program was fine, then I started using FindRootPlot, but it didn't work well so I removed the line and went back to using FindRoot and it gave me some crawl errors ...
14
votes
4answers
459 views
NDSolve giving a wrong solution
Consider the ODE
$$\frac{y'y}{1+\frac{1}{2} \sqrt{1+ y'^2}}=-x.$$
Using
NDSolve[{-x==y'[x] y[x]/(1+Sqrt[1+(y'[x])^2]/2), y[0] ==3}, y, {x,-7,7}]
and plotting leads ...
0
votes
1answer
63 views
Solving integral equation with CDF
I would like to manipulate a functional equation where $F$ is a cumulative distribution function, which I would let Mathematica know.
Using a simple example, consider
$$(\rho + \lambda\overline{F}(w))...
0
votes
0answers
45 views
How to work with a function in vector form
I would like to use Mathematica to compute the X and Y elements of the vector on the left (below) for various t values and put result in a column vector form? I used Mathematica's palette to write the ...
1
vote
1answer
26 views
Intersection point for existing solution - avoiding error messages, message in diagram if no solution exists
I am trying to highlight the intersection if one exists. For specific parameter values there is no solution and the manipulate output creates error message and red background.
How can I avoid the ...
3
votes
2answers
224 views
System of equations does not solve with Solve
I am trying to find the solution in order to highlight the intersection point.
...
2
votes
5answers
380 views
Implementing Newton's Method?
For an assignment, I have to implement Newton's method using
Module and a For loop. So far, I have
...
0
votes
3answers
47 views
Solving equations with complex or real or imaginary number
GG = {N3*Conjugate[N3]+ N4*Conjugate[N4] == 1, (2 N3 + (-I + Sqrt[2]) N4)/(2 Sqrt[3]) == 0};
Sols = Solve[GG, {N3, N4}]
I need to solve the above equation. But I ...
0
votes
1answer
39 views
Intersection point across two diagrams with manipulate: Problems with Coordinates
I am trying to highlight the intersection point (point, dashed lines) in the bottom diagram and the the corresponding point in the top diagram. Unfortunately, I am creating lots of error messages in ...
0
votes
1answer
44 views
Using Solution to Differential Equation in New Function
I am trying to feed the solutions from my differential equations into another function.
I am using NDSolve to solve two differential equations simultaneously. It ...
5
votes
0answers
169 views
Finding periodic cycles of a function
Given a function f[{x,y}] it is rather simple to use, for example, NSolve to find periodic points of period $n$. We simply take ...
0
votes
1answer
67 views
Solving an exponential inequality in two ways
I would like to solve the following inequality E^x/x^1000 >= 2 without Reduce.
Then I would like to solve it with ...
1
vote
4answers
62 views
Solve function used symbolic computation yields all the coefficients value zeros
I am trying to compute the symbolic coefficients of using Solve function. But this is yielding all the coefficients values zeros. What are the other ways to find ...
1
vote
1answer
42 views
NSolve failing to find the roots of an transcendental equation
Why NSolve is not working for this problem. By plotting the determinant equation it is clear that there are roots between 5 t0 10, but ...
1
vote
0answers
53 views
-2
votes
0answers
29 views
Getting message Solve::itdim
When I use Indexed and solve an equation, I get the error message:
Solve::itdim The dimensionality of variable p is not well specified
My code is:
...
0
votes
0answers
46 views
Making a equation smaller and more readable by using another variable [duplicate]
I am deriving an expression and the output of it is a very long mathematical expression. I want to minimize the equation by substituting some other variables. For example:
This is just an example ...
1
vote
0answers
18 views
“NDSolve::femper” Error in Solving Coupled Nonlinear PDEs [duplicate]
For example, consider the following piar of PDEs with two unknown functions $u(x,y)$ and $v(x,y)$:
$$
\partial_x^2 u+\partial_y\left(v\partial_y u\right)=0\,,\quad\partial_x^2 v+\partial_y\left(u\...
1
vote
0answers
59 views
Solving $E[abXab]=Y$ for Gaussian $(a,b)$
I have $d/2$-dimensional variables $a,b$ jointly distributed as Gaussian($\mu,\Sigma$) in $d$ dimensions, and need to solve the following equation for $X$
$$E[ab^TXab^T]=Y$$
This is equivalent to ...
2
votes
3answers
414 views
0
votes
0answers
47 views
solving coupled nonlinear differential equations
I have defined a table containing 3*3 matrices
a1 =Table[Array[
Subscript[Subscript[ρ, i], #1, #2][t] &, {3, 3}], {i, 1, 3}]
Then I define another 3*3 ...
1
vote
1answer
76 views
A simple problem that occupies too much time
I'm trying to get Mathematica to solve the following system, consisting of two identical equations, except that the variables z1, u1, u3 (in the first) and zz1, uu1, uu3 (in the second) represent ...
0
votes
0answers
19 views
I want to use the output of Solve and/or Reduce in next steps. But the output comes in the form of a rule [duplicate]
In a program I want to use the output of Solve and/or Reduce in next steps. But the output comes in the form of a rule, where what I want is the numerical solution. Here is an example. Say I write s=...
3
votes
1answer
91 views
Need help with a linear programming problem
Consider
$1\rightarrow{}x+2y\leq{500}$,
$2\rightarrow{}2x +y \leq{520}$,
$3\rightarrow{}2x+5y \leq{}1200$,
$4\rightarrow{}x \geq{}0$,
$5\rightarrow{}y \geq{}0$,
The above is the set of inequalities ...
3
votes
2answers
81 views
Specific problem with NDSolve step size, stiffness
I am trying to solve a non-linear second order boundary value problem in a finite interval. The differential equation is $$y''-\frac{a}{b}y-\frac{u_n}{b}y^3-\frac{ge_0}{b}x=0,$$ with $x\in[0,L]$, ...
0
votes
0answers
138 views
Not understanding the reason for not getting full rank matrix
I have a structure shown in figure. It has four members. Each member has represented by two displacement field $W_i$ and $U_i$. I have expressed this displacement field using some functions. I found ...
2
votes
1answer
61 views
NDSolve with a 0/0 error
I am trying to solve this set of coupled first order differential equations. The $\phi'$ term gives a 0/0 error for when $\epsilon=0$. When I enter:
...
0
votes
1answer
27 views
Solving a large system of equations for the smallest integer values
I'm trying to find the smallest possible non-negative integer solutions to hundreds of fairly large equations systems . An average example would be the following:
...
0
votes
1answer
27 views
1
vote
0answers
60 views
Assuming a monotonic function
I'm trying to tell Mathematica that a function is increasing. More specifically, I would like at least one of the following statements to report 'true'.
...
0
votes
3answers
66 views
0
votes
1answer
79 views
How to solve the Summation equation by FindRoots [closed]
I want to find out the value of alpha and lambda where u lies between 0 and 1.
