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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1answer
86 views

Solving infinite coupled equations

I need to solve symbolically an infinite system of coupled algebraic equations that I tried to do analytically but I could not. Solutions of these equations, $V_l^m$, define the coefficients of a some ...
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3answers
42 views

Optimizing with respect to the parameters of an optimization problem

I’ve got this simple loop that prints out the solutions to 2 simple equations for various values of parameters $a$ and $b$. I need to add a command that would display the parameter values that lead ...
1
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1answer
43 views

Find the intervals where a piecewise is maximum

I have the following 3 piecewise functions and I would like to have the threshold of the upper envelope. ...
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1answer
32 views

remove one of the column in the output of Solve command

I would like to remove one variable in the output of the "Solve" command without changing the rest. For instance, in the following code ...
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0answers
33 views

Analytic maximization that reduce fails to solve

I'm working on an interesting problem but stuck on a step that Mathematica fails on (no matter what angle I try to get at it from). I'm attempting to find the symbolic maximum of this convex function ...
1
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0answers
49 views

Solving an algebraic-differential equation

I cannot find the relevant part in the documentation. Maybe you have a quick solution to my problem. Background Sometimes you want to propagate in time some system of ODEs, but not all the variables ...
1
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1answer
38 views

Symbolic equation pair with two unknowns [on hold]

I am a beginner with Mathematica, so hopefully my problem is clearly presented. My problem is solving two unknowns from equation pair with five symbolic parameters. Baghdadi et al. (2016) created ...
1
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1answer
37 views

Solve to model an insurance linked security

I want to model a simple reinsurance program, sometimes referred to as an insurance linked security. The inputs to the model include: program, the cost of an ...
0
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1answer
83 views

FindRoot: Power: Infinite expression 1/0. encountered

I am trying to solve the problem below with FindRoot. At first it works well, but when I change the constants in my equation the solver returns with the message: ...
0
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2answers
56 views

Get the derivative function plot from a NDSolve solution

I been trying to plot the derivative function of j[t], being j'[t]. Here a look to the code. I would appreciate your help. Thank you ...
9
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3answers
948 views

How can I solve for the intersection points of two ellipses?

I need to find the points at which the two ellipses implicitly defined by $\qquad y^2=4-4\,x^2 \quad[E1]$ and $\qquad (1-(x/2))^2+(y-1)^2=1 \quad[E2]$ intersect. So I isolated $y$ in E2 and ...
0
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1answer
28 views

Remove inequalities from set of rules

I solved a set of equation and use reduce on the set of solutions. Changing the equal sign to arrows I get some set of rules but some of the entries are inequalities. E.g. ...
0
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1answer
54 views

Solving a profit maximization with Cobb-Douglas production function

I'm considering a typical profit-maximization problem: \begin{equation} \label{optimization1} \begin{aligned} & \underset{K,L}{\text{max}} & & P Y - r K - w L \\ \end{aligned} \end{...
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1answer
34 views

diagonalisation of systems of symbolic equations from two cross products

A description of what I'm attempting: Given a generic vector $\vec{r}$ and a point in space $D$, I want to build a reference frame centred in $\vec{r}= (x,y,z)$, with one axis directed along the ...
1
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1answer
66 views

How can I solve this equation for the exponent n?

How can I solve: $$(a^{n-5/2}-b^{n-5/2})=c$$ for $n$? $a$, $b$ and $c$ are known constant. It seems that Solve cannot solve it and ...
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0answers
34 views

How to find the value in which an expression becomes greater than another

I have the following expressions: $\Delta \sigma_1=\frac{2 \gamma ^2 \left(\text{$\sigma $Y} \log \left(\frac{\gamma }{\alpha }\right)+\text{pe}\right)}{\left(\gamma ^2-1\right) \rho ^2}$ $\Delta \...
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0answers
92 views

Calculate the intersection points of a line and a parametrically defined 3D surface

Thanks to Henrik Schumacher for advice to simplify the sample code: I would be grateful for any pointers on the following issue. A line from an external point intersects the surface at 2 points (...
3
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2answers
206 views

Solve equations with condition on variable to reduce the number of solutions

I'm trying to solve an equation, and while it work, "plain" Solve returns two solutions that are, in the specific case, of no interest. ...
2
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1answer
45 views

Solving a system of nonlinear equations with parameters

I try to solve a system of two nonlinear first-order conditions for the variables $\phi_{A}$ and $\phi_{B}$ with two parameters $\alpha, \beta \in (0,1)$. Please see example code below. I am looking ...
1
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1answer
45 views

Mathematica not giving exact answer for Solve [duplicate]

I'm trying to find the maximum value of d[x_]:=4-(1/5)x^2-3*Cos[Pi*x/6] For -5 < x < 5. Aside from x=0 which is a local minimum, when I use Solve, I can ...
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0answers
48 views

Function of square roots returns value with 0 imaginary part

I am considering the following function called funAl: 1/2 (1 + (Sqrt[3] Sqrt[868 - 1700 xi + 825 xi^2])/Sqrt[4 - 25 xi^2]) This function occurs as a boundary in ...
2
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4answers
242 views

How to derive trigonometric Cartesian equation from parametric

How can one derive programmatically a Cartesian equation when $x$ and $y$ are parametrically represented by trigonometric functions? i.e.: Given that $x= \cos(2 t)$, and $y = -\sin(t)$, how can I ...
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0answers
43 views

FindInstance Returns “Aborted” [closed]

Edit: Apologies, the question needs to be reworked, because I cannot reproduce the original problem using this code. I don't delete the question, in case someone is preparing an answer at the moment. ...
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0answers
36 views

InverseFourierTransform takes me forever

I am trying to solve complicated PDEs using FourierTransfrom and InverseFourierTransform on Mathematica 12.0, but the code below does not give me a result. I do not get any error messages but the ...
7
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2answers
669 views

Solve equation using Mathematica

I want to solve this equation using Mathematica: $$ 4^x -18^x-8=0 $$ I tried this code and it didn't work: Solve[4^x-18^x-8==0,x] Please help me.
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1answer
66 views

WhenEvent error in NDSolve ODEs

I wish to change the term, T'[t] to 0 when S[t]<=0 when I solve ODEs. I have used WhenEvent in my NDSolve part, but it seems not work. The code is ...
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2answers
34 views

Correctly restricting domain of parameters within Solve

I have seen a few posts about this (such as this one), but none solved my problem. As a silly example, suppose I want to solve (1-x)^n = 0, knowing that n > 1. I ...
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1answer
21 views

Solving system given specific inputs

I am solving the following system with given inputs for x', q, d, x[0], and y[0]: ...
2
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0answers
62 views

How to efficiently solve a large system of equations

This question is a follow-up of my last question. Summary The user Henrik Schumacher gave an excellent answer about how to store equations efficiently and solve the associated homogeneous system by ...
2
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1answer
32 views

NDSolve error with manipulate for 2 coupled ODEs

While trying to solve a system of coupled ODEs (for EVE[t] and FTZ[t]) with Manipulate, I ...
5
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0answers
43 views

Limitations in using Reduce for Integer systems

The System For example, when solving the following system using Reduce in Integers: ...
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0answers
44 views

Calculation by hand different form Mathematica Simplify function

I look at ClearAll[x, y, t, q, d]; Simplify[ 0 == 1 - d x[t] - (3 + 2 d) y[t], 0 == 1 - d y[t] - (3 + 2 d) x[t]] When I solved this by hand, I found that x = y ...
10
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3answers
155 views

Confirmed Bug: Why does Eliminate fail while Solve succeeds?

OP EDIT: Wolfram Technical Support got back to me and confirmed this is a bug. But the Answers below provided good workarounds. I have two polynomials respectively in {z,c} and in {r,z,c}. I'd like ...
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3answers
53 views

Instability of FindRoot solution

Using FindRoot on a smooth function of a parameter and a variable, the resulting solution should be a smooth function of the parameter, by the Implicit Function ...
0
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0answers
24 views

Limited integer domain in Mathematica Reduce function

I want to solve a system of equations in Mathematica where all variables are restricted to be integers between -3 and 11. Which ...
0
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1answer
24 views

Error Code 414 while trying to do a substitution

I was trying to see what would happen if I let d=q in the following equation: ...
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0answers
34 views

How to convert output from Reduce into a piecewise function?

Reduce often provides a much fuller solution than Solve. But it's always in the form of a true statement rather than functions ...
1
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3answers
58 views

How to solve that complicated equation with parameter?

I try to solve for "t" at the various "x" from the function of ...
1
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2answers
48 views

Solving System of Ordinary Differential Equations (ODEs)

When I input the following code to solve this system of equations (I specifically want to look at 0<d<1, 0<q<1, 0<t), I get the error: 'DSolve: The ...
0
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1answer
47 views

How to find x from expression? [closed]

I need to find x in this expression x(2x + 5) = 168 I have already tried to move x from one side to another with brackets and without them, Like this x = 168; 2x + 5 = 168 , 2x = 163 , x = 81.5......
2
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1answer
91 views

Long Execution Time of Reduce

I have a set of linear homogeneous equations with 8580 variables. I want to estimate the time Mathematica takes to solve the system, by solving smaller sets of ...
0
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1answer
29 views

How can I get paired coordinates from the implicite function?

I have equation E^y = x. How can I use Mathematica to solve all of "y" from the desired "x" value. For example, I want to solve for "y" from x = 0.5 , 1 , 1.5 , 2 , .... , 9.5 , 10. The solution ...
2
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0answers
67 views

How does Mathematica Find Integer Roots For Certain Transcendental Functions?

I have these two equations: $$f(x)=(\cos(\frac{n}{x} \pi)\cos(x\pi))-1$$ and $$g(x)=\sin^2(\frac{n}{x}\pi)+\sin^2(x \pi)$$ where $n$ can be any integer. These two functions are what mathematicians ...
0
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0answers
37 views

Solving Inequalities: Run time too long

I am trying to solve the following system for d: ...
1
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1answer
45 views

Solve coupled PDEs: boundary conditions problem

I need to solve 4 coupled PDEs. Thanks to @xzczd's help, a few days ago I can obtain the solution of the first 2 equations with some proper boundary conditions, see this post. Now, these two equations ...
2
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1answer
64 views

Solving for a function?

I am trying to find an ‘elegant’ manner of expressing the need to solve equations of the form f[f[n]]=-n. I’ve been tackling this as a power series expansion but I ...
1
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1answer
66 views

Solidification Problems in MMA

can we define such intial value and BCs for a solidification problem in MMA using Finite Element: 1.) initial value:=1 for a plate 2.) in this plate we have to define dirichlet bcs for a whole ...
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0answers
39 views

How to solve this trigonometric equation

The equation Sin[9 x - Pi/3] == Sin[7 x - Pi/3] can solved by hand Reduce[9 x - Pi/3 == 7 x - Pi/3 + k 2 Pi, x] x == ...
5
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1answer
89 views

Should Reduce give all cases when $\sqrt{x y} = \sqrt x \sqrt y$?

My understanding is that Reduce gives all conditions (using or) where the input is true. Now, $\sqrt{xy} = \sqrt x \sqrt y $, where $x,y$ are real, under the ...
10
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2answers
277 views

Solving Cahn-Hilliard equation: LinearSolve: Linear equation encountered that has no solution

I have built the Cahn-Hilliard Eqs. in MMA (Mixed Formulation, second order), However, it doesnot work in MMA using Finite Element. LinearSolve: Linear equation encountered that has no solution. And ...