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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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 ...
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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 \...
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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]: ...
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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 ...
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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 ...
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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'. ...
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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 ...
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2answers
52 views

Using a list inside NDSolve

I have a coupled differential eqations: ...
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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 ...
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1answer
58 views

Can't find the correct root for this equation

So I have this expression ...
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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 ...
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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?
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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(\...
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1answer
33 views

How to make sure the answer is limited to Positive Reals?

As the title described, there is code: ...
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0answers
41 views

Solving quadratic eqaution with many parameters [closed]

It seems like Mathematica or my PC has problems to handle long equations: ...
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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 ...
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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, ...
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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: ...
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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 ...
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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 ...
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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))...
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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: ...
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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 ...
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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\...
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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 ...
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3answers
414 views
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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 ...
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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 ...
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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=...
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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
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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 $x\in[0,L]$, ...
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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
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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: ...
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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: ...
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1answer
27 views

Reducing solutions from Solve to positive solutions

Consider the following lines; ...
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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'. ...
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3answers
66 views

Solve for matrix in linear equation

I need to find a matrix M such that M.u = v, where u and ...
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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.

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