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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Finding a functional form, solving a differential equation

I am giving my actual problem, but I would also like to understand how to solve such problems in general. I am neither a mathematician nor do I know a lot about Mathematica. I am looking for a ...
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1answer
37 views

How can I solve this inequality for every $n$ in Mathematica?

I am trying to find the solution to the inequality $t^{-1/n}<1$ when $n$ is an integer and $t$ is positive, however when using Reduce[t^(-1/n) >= 1, t] it ...
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1answer
84 views

How can I simplify my geometric calculation?

Here is a math problem I am dealing with right now: Given ellipse $C$: $x^2/a^2 + y^2/b^2=1$ ($a>b>0$). Ellipse $C$ passes through the point $P$: $(1,3/2)$, and has eccentricity $e=1/2$. ...
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1answer
65 views

Obtaining a parameter using Brent's method

Using Brent' method, I want to find a $g$ which minimizes $\Delta$ that is defined as $$\Delta=\sum_{n=1}^N F^2_n \tag{1}$$ where $F_n$ is $$ n(n-1)\mu_{n-1}+2Z\mu+2E\mu_{n+1}-2\alpha\mu_{n+2}-2\beta\...
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2answers
117 views

1DPoisson equation with Dirac delta

I was writing my own FEM method to solve the Poisson equation \begin{align} -u'' &= \exp(-c(x-1/2)^2)\\ u(0) &= u(1) = 0 \end{align} where c=100. and I'm reading from the book of Mats G. ...
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36 views

Solving a large linear system

I have a system of 12 equations with very large symbolic expressions but linear in some variables that I want to solve it for. I have been running Solve for many ...
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1answer
76 views

Solving a well known transcendental equation [on hold]

Evaluating Solve[E^(n t) == Cos[t] + n Sin[t], n] does not produce a solution for $n$. What method should be used to solve for the value of $n$?
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1answer
39 views

Solve returns complicated and wrong solution

I have the following equation (8 F (D1 + ((D2 - D1) nf)/n)^3)/(G d^4) == H/n Solving for $n_f$ by hand is simple and gives $$ n_f=\frac{n}{\text{D2}-\text{D1}} \...
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1answer
38 views

points of intersection along curve and horizontal line [duplicate]

I'm trying to find the intersection points of the following plot with the given boundaries. How would I do so in the bounds set by the above plot? I've tried FindRoot by setting the lines equal to ...
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1answer
55 views

NSolve for x and y

I'm trying to solve the following for x and y, but the evaluated cell just gives me back what I tried to solve, just a little more simplified. If both x and y were bounded from [0,5], how would I ...
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2answers
61 views

Find best fitted approximated parameters

I want to find the best fitted approximated parameters for the following case: $$\begin{align*} 2a + 3b &= 5\\ a + b &= 4\\ a + b &= 3.9\\ 2a + 3b &= 5.1 \end{align*}$$ When I use <...
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1answer
46 views

solve equation by explain n*n matrix or equation team

I want to solve n equation which has n root with Gauss-Elimination Method. I indicated root formulation and methodology in picture. But I don't know that how can I do this. Should I explain n*n matrix?...
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3answers
84 views

How to print by using For loop? [on hold]

For[mu = 0; mu < 6, mu++, mu = -4.84*10^(-4) - 17.82*10^(-4)*T1 + 1.53*10^(-4)*T1*2.303*Log[T1]; Print[T1]] I want to get the value of ...
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0answers
39 views

Never terminating when solving linear Diophantine systems

Say I have: $(1):$ Set of Diophantine systems where each defines a (possibly unbounded) polyhedron. This is solvable with existing algorithms: $(*):$ The $(1)$ can be solved in SageMath with ...
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0answers
37 views

How robust are mathematica‘s equation-solving capabilities? [closed]

My question regards using the Mathematica command as part of a rigorous proof. Rather than describe the general situation—- suppose I can the proof of a result to the fact a pair of equations $h(a,b)=...
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33 views

Is there a feasible computation?

I have to find the values of $p_1$ and $p_2$ which minimizes the expression $G$. However, when I took the partial differentiation of $G$ with respect to $p_1$ and $p_2$, the equations I obtained were ...
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4answers
94 views

Unable to find root for user-defined function

I created the function getSolution[xVal,yVal] for a geometry problem I'm working on and wish to solve it for getSolution[2,x]==0. I can plot it clearly showing the roots: However, when I attempt to ...
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3answers
147 views

Mathematica Fails to Solve a System of 3 Equations!

I'm trying to solve what I thought would be a simple set of 3 equations for Mathematica! But it grinds endlessly without any result.. ...
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0answers
22 views

NIntegrate in FindRoot: s=S is not a valid limit of integration

I get an error code saying that "s=S is not a valid limit of integration" when I use the following code: ...
2
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1answer
39 views

How to find the distances between two adjacent maxima in a solution from NDSolve

I try to find a general approach to plot the time evolution of horizontal distances from maximum to maximum in a solution of PDE. The solution u[x,t] normally have ...
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0answers
112 views

Need help with ParametricNDSolveValue for ODE with two variables and Do-loop

I' m trying to solve a tricky 2-nd order ODE with ParametricNDSolveValue for boundary conditions (BCs) y = 0 at R and ...
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2answers
48 views

how to solve the equation

I want to sole the given equation for x. Can anyone help me please to analyse the solution. Thanks ...
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3answers
99 views

Solving 5 nonlinear equations, is there a suitable way?

I'm trying to solve a set of 5 nonlinear equations using NSolve: ...
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1answer
31 views

FindRoot: equation with integral on parametric domain

Writing: ...
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1answer
47 views

Need help with ContourPlot3D

I need to print out the value of x, y, and z when h==0, g==0. Help please? ...
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1answer
90 views

Solve giving solution when there is no solution

I got a strange result from Solve. I have the following relations: ...
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0answers
34 views

Getting an analytical form $f(x,y)$ from numerical solutions of a ContourPlot

I numerically solved a set of equations which yields a solution of the form $f(x,y)=c$. I was hoping to obtain an analytic expression for $f(x,y)=1$ (in my case $c=1$) but all I managed to do was to ...
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1answer
132 views

Solve a one dimensional heat transfer problem with NDSolve

The following problem is a 1-D heat transfer conduction problem: where, I am trying to solve with NDSolve like this way: ...
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1answer
47 views

How to ask Mathematica to express variables in terms of each other in an implicit function

How to ask Mathematica to give $y$ in terms of $x$ in this function? Is there a way to obtain a closed form expression for $y$ in terms of $x$? $x=\frac{\left(y^4-1\right) \left(\coth (2 y)-\frac{1}{...
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0answers
57 views

Why does FindInstance take so long: It is faster with more restrictions than with less?

A support case with the identification [CASE:4347836] was created. I just noted this little puzzle on twitter by Brillant.org: \begin{align} A B C\\+ BCA\\ = CDE \end{align} Given that $A$ is even ...
14
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2answers
304 views

Convert symbolic to numeric code: speed up morphing

Recently I asked a question about the morphing between two functions and got two excellent answers. The accepted answer is using the continuous optimal transport theory. This seems to be very suitable ...
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0answers
27 views

Simulating a function with no closed form solution

So I am trying to simulate a function in 3d. Suppose our function looks like this: f=k*r*a I am interested in simulating the numerical values of k when r is ...
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2answers
35 views

Manipulation replacements rules from Solve [closed]

Assume the call to the routine Solve[eqn==0,{x1,x2}] returns: {{x1->a1,x2->a2},{x1->b1,x2->b2}} I would like to ...
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2answers
79 views

Verifying that a functions attends values below something

After plotting the graph of $$f(x)=\frac{π}{3\sqrt{2 π}} (\frac{e^{\frac{-x^2}{18}}}{3} + \frac{e^{\frac{-(x - 5)^2}{2}}}{1} +\frac{e^{\frac{-(x - 15)^2}{8}}}{2} ) (1 + x^2)$$ I would like to ...
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0answers
41 views

Solving an equation: Reduce command produces failure message

I am trying to solve the following equation for c: All variables can only take positive values and c>s. I have tried the following code: ...
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0answers
28 views

Reduce[expr,vars] behavior when vars are not present

It is officially documented that Reduce should be used like Reduce[expr,vars]. However, I've used ...
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0answers
66 views

How do I solve a cubic equation for values of x?

I have partially differentiated an equation w.r.t. x, see picture below, and want to isolate x in the equation to solve for a local maximum. Can I use Mathematica to get it on a cubic form? and how ...
2
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1answer
141 views

Why FindRoot does not give all roots? [closed]

I would like to solve complicated equation and use FindRoot to find roots numerically. I do not understand the following problem. I provide the simple example. Considert the equation: ...
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1answer
49 views

Hardy Ramanujan Question [duplicate]

I revised the code I asked about earlier, but I am still not getting an output. According to Mathematica it is (mostly) correct syntax. Here is the revised function: ...
2
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0answers
34 views

NMinimize with real solutions, problem in the resolution and criteria for other ways to solve equations

I have multiple parts in my question. You are welcome to answer to any of them :) Part 1 : I have 3 equations $p(x_1,y_1)=p(x_2,y_2),\mu_x(x_1,y_1)=\mu_x(x_2,y_2),\mu_y(x_1,y_1)=\mu_y(x_2,y_2)$. I'm ...
10
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1answer
287 views

Numerically solving a system of many coupled non-linear ODEs efficiently?

I'm studying a fairly typical problem: a chain of $n$ coupled, non-linear oscillators. Since I want to look at open boundary conditions, the equations of motion for the position of the first and the ...
3
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3answers
38 views

Using Element on list of numbers when defining equations

If been looking on how to construct equations with region or domains for some variables. Suppose I have x and that x can only be the number 1,2,4 or 7 The equation 2 x < 10 will then results in x ...
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1answer
49 views

NDSolve for Complex Algebraic-Differential Equation

Let consider the following complex equations: $$ \frac{i x(s)}{2\pi} - \frac{\log(1+ e^{-y(s)}) - \log(1 + e^{y(s)})}{\dot x(s)} $$ which I will cal eq1 and $$ \...
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1answer
70 views

How this equation is solved in reals

I have tried to solve this equation $2^{-2 ^{2^{-x}}}=2$ using FindInstance[2^(-2^(2^(-x))) == 2, x, Reals] The result is ...
2
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1answer
83 views

Efficient way to list zeroes of an oscillating function

From "The First 50 Million Prime Numbers" by Don Zagier: primes are integral roots of$$ 1-\frac{\sin(\frac{\pi\Gamma(s)}s)}{\sin(\frac\pi s)}. $$ The graph of this function looks like I would like to ...
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0answers
45 views

Roots of complex numbers

My exercise is to find $n$ roots of a rank $n$ of a complex number. Here is my code: ...
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1answer
54 views

Is priority important in `Series` expansion?

I have a strange case here! The story begins with this equation ...
3
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2answers
169 views

Strange NSolve failure [duplicate]

...