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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2
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1answer
111 views

Two first order non-linear differential equation: Using DSolve to obtain the solutions analytically

I have two simple first order (coupled) differential equations which I denote as system together with its initial conditions ...
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2answers
56 views
2
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1answer
60 views

Three Coupled ODEs

I've been trying to solve it with Mathematica Order of DSolve but I'm not getting Anywhere! so if anyone got an idea i would be glad to tell me how to get answer p.s:I just want solution and Numerical ...
0
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1answer
44 views

How to solve for the velocity? [closed]

Given the equation: $m \dfrac{\mathrm dv}{\mathrm dt} = m g_{e} - \beta v^{2} $ the velocity evaluates to $ v(t) = \sqrt{\dfrac{m g_{e}}{\beta}} \tanh \dfrac{t}{\sqrt{\dfrac{m}{\beta g_{e}}}}$. In ...
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0answers
48 views

DSolve with initial conditions

I am having trouble solving differential equations with initial conditions, and unfortunately the answers given in similar questions in this forum don't seem to work for me. My final goal is to solve ...
1
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1answer
99 views

How to solve a non-linear equation

I want to solve an equation $$\log \left(\frac{b}{y}\right)=\left(\frac{x}{y}-a\right)^{\beta}.~~~~~~~~~(1)$$ Solve[Log[b/y] == (x/y - a)^\[Beta], y] Here $b$, $x$,...
2
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1answer
153 views

How to symbolically solve this transcendental equation

The equation below shows up when dealing with geodesic curves on elliptic paraboloids: \begin{equation} u-c^2=u(1+4c^2)\sin^2\left(v-2c \ln\left(k(2\sqrt{u-c^2}+\sqrt{4u+1})\right)\right) \tag{1} \...
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0answers
35 views

Solving a system of inequalities where some of the variables are integer-valued, and some are real-valued [closed]

I'd like to know how to ask the Reduce command to solve over one domain for certain variables, and another domain for other variables. For example, I'd like to solve the system of inequalities $$ 2 a +...
1
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1answer
66 views

How I found the value

I would like to know how to find the value of a function. For example, consider one the most basic funcions y[x] = x^2 The ploy is a parabola. So if I want y = ...
7
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1answer
121 views

Extract Jacobian from FindRoot?

I have to solve a system of fixed point equations and then calculate the eigenvalues of the Jacobian at the fixed point. There are about 50 equations with 50 variables and they contain a lot of ...
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0answers
51 views

How to judge the number of real roots of polynomials?

If $3 a^{2}-5 b<0$, how many real roots does the polynomial $x^{5}+2 a x^{3}+3 b x+4 c=0$ have? Discriminant[ x^5 + 2 a*x^3 + 3 b*x + 4 c, x] I want to know how ...
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0answers
24 views

Why doesn't mathematica recognize the exponential expression with Solve but it will plot it written exactly the same way? [duplicate]

I can Plot these two functions written exactly this way and see intersection but Solve will not recognize the exponential expression. Please help me with feedback... Solve[1/3Exp[-x/5]==Cos[x], x]
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1answer
112 views

Coupled second order differential equation with NDSolve

I am trying to solve a 2nd order ODE to reproduce a plot. Here are the equations: ...
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0answers
97 views

Equation of Parabola through Four Points

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0answers
50 views

Returning complex numbers when it's supposed to be real numbers

So I am trying to solve the following polynomial ...
0
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1answer
63 views

the solution of this equation comes in terms of Roots and i don't know how can i simplify this solution please help me [duplicate]

Solve[(u (Sqrt[8 p] - 3 Sqrt[u])^2 (Sqrt[8 p] Sqrt[u] - 2 p - 3 u))/( 2 (Sqrt[u] - Sqrt[8 p])^2) + (2 p)/3 == 0, u]
2
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1answer
67 views

Difficulty when trying to find roots to high accuracy

I'm working with the logistic map $f(x,\lambda)=4\lambda x(1-x)$, and iterations of the logistic map $f^{(2^n)}(x,\lambda)=f^{(2^{n-1})}(f^{(2^{n-1})}(x,\lambda),\lambda)$. There are some special ...
0
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1answer
50 views

How do you convert an ordinary equation into a parametric equation? [duplicate]

It's a 3D linear equation {P1: 2x-y-3z+2=0,P1: x+2y-z-6=0} Are there any methods that can convert this linear equation to its parametric form. Ps:the parametric form is {x=7t, y=-t+14/5, z=5t}
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1answer
41 views

Find relationship between values within finate range of integer domain

Update: There are some misakes in the coefficient of left and right. But still get similar result. I understand the mathematica ...
2
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1answer
60 views

Find the best pair of whole numbers that gives a real solution for a system of equations

I have a system of equations given by: ...
-3
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1answer
92 views

How to solve those equations [closed]

Question 1: I want to find the expression of the function f[x] of the following equation: ...
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0answers
83 views

Determining Choices for Solution of a Matrix Equation Through NullSpace Function

I am trying to see how Mathematica chooses the basis vectors of the nullspace computed through: ...
1
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0answers
46 views

Problem with logarithmic equation

I'm trying to solve the following equation and get an error in Mathematica. ...
0
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1answer
64 views

What can I do to get Mathematica to solve this equation?

I am trying to solve an equation on Mathematica 12.1 to get angles in radians as part of some analysis: ...
9
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3answers
398 views

Why is the solution I obtained from Solve not verified in the original equation?

I have this equation $$x^2 \left(\sqrt{1-y^2} \sin (x)-\sin (4 x)\right)+2 x y=0$$ I want to solve this equation and find $y$ in terms of $x$. I use Solve ...
3
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1answer
222 views

Equation with logarithms, why it can't be solved?

I'm trying to find the -3 dB frequency of a filter in Mathematica. Yet, my code doesn't seem to work as it produces imaginary values for the frequency. ...
2
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1answer
78 views

Least common multiple and greatest common divisor problem.What instruction to use?

Here we have an equation in two variables that involves the greatest common divisor and the least common multiple, I can't think of what else to use. $$Reduce[(LCM[x, y])^2 + (GCD[x, y])^ 2 == 900]$$ $...
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0answers
45 views

RegionPlot outputs System`ReduceDump`

I'm using Solve[] to find the solutions to a system of equations, then checking their stability in a Hessian using ...
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3answers
101 views

Plot multiple (all) solutions of Solve as function of parameter

I have a nonlinear equation that may have different number of solutions, dependant on parameters. ...
6
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3answers
248 views

How can I find the criteria for a polynomial to have, and only have, double roots?

In the help document of function SolveAlways, I saw the condition that a polynomial has a triple root. ...
0
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1answer
28 views

How to find multiple groups of solutions that meet the requirements

I want to find multiple nonzero real matrices A, B that satisfy $A.B=\mathbf{0}$ condition. ...
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0answers
26 views

Series Expansion Using Results from Reduce

I have a list of relations from using the Reduce function and I want to use them to get a series expansion in each variable. Here's what my relations look like: ...
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0answers
29 views

Iteratively Expanding Solutions in Multiple Variables

I've been working on a physics problem which requires finding the limiting behavior of variables as another variable goes to either zero or infinity. What I have is relations between 16 independent ...
2
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1answer
62 views

Solving complex differential equation with ParametricNDSolveValue

I am trying to solve a complex differential equation for the function $S(u,v)$ depending on the parameter $\omega$. The code is: ...
0
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0answers
40 views

AsymptoticSolve and Series not working in limit $\to \infty$. How to solve this functional polynomial relationship?

I want to solve for $J_d$ as a function of $n_d$ for $\eta\gg1$ and $\eta\gg\eta_0$ in the following equations by eliminating $\eta$ from the two equations. \begin{equation} J_d = J_0\cdot\left[\...
1
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0answers
33 views

Solving coupled PDEs using NDSolveValue

Im very new to Mathematica and trying to solve a model of two PDEs. The system contains two components that get generated after T=0.5 and diffuse away and dissapear at either end (If I've described it ...
1
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2answers
91 views

Best way to solve stupidly complicated parametric non linear equation with reduce/solve etc

I have a parametric nonlinear function which is literally a nightmare. I know roots exist, they are real and the two parameters, p,e are both positive. What I was ...
4
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1answer
83 views

Find intersection points of arbitrary BSpline curve

I'm researching some computational geometry and am trying to find a method of determining the {x,y} intersection of a circle and BSplineCurve for further processing. ...
0
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2answers
68 views

Solve can not solve the equation correctly in Reals

Here is the error I found. r = 3; Solve[Sqrt[(r^2 Cos[m Pi] - x)^2 + (r^2 Sin[m Pi])^2] == 10 && x > 0 && 0 <= m <= 2, x, Reals] ...
-1
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1answer
61 views

A series of factors or an equation? [closed]

Is there anybody that can help me simplify the following ideas in an equation, a series of factors or whatever mathematical form is easier to later use and understand? They all have to be true. 🙏 x = ...
0
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2answers
51 views

Solving parametric function numerically for positive values

So I have a function f1[x,y] that includes a parameter c. I would like to solve the corresponding ...
0
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1answer
117 views

How to find a solution of this matrix equation quickly

I need to solve the following matrix equation to find a set of solutions for matrices A and Q which satisfy the conditions. <...
0
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0answers
47 views

Why does specifying the solution domain seriously affect the solution speed?

I want to solve the problem of this post. After trying, I found a strange problem. When I specify the solution field as a real field, the code runs all the time: ...
3
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1answer
134 views

Stiff System of ODEs: NDSolve Convergence Issues

I have tried to use NDSolve for solving 4th order coupled ODEs problems (see the attached codes). The MMA solver fails to solve this problem. ...
0
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1answer
73 views

How solve nonlinear equations by 14 unknowns?

This is my code, i want to solve system by 14 equations and 14 unknowns(rr list).But the code doesn't run... ...
0
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0answers
55 views

How to find and split two surfaces made of roots of a determinant?

I have a matrix from which I want to find the roots for different values of [Delta]g0, [Delta]d0 and [Epsilon]. I know there will be a maximum of two roots for a set for a set of parameters and after ...
1
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3answers
259 views

Problems with solutions involving Lambert W function of transcendental equation

Solve and Reduce fail here with rational parameter l, but succeed when I plug in a value <...
0
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2answers
117 views

How to quickly find a set of solutions that meet the requirements

Note: The following questions are from the 21th question of the 2010 Chinese Graduate Mathematical Entrance Examination (first set): It is known that the canonical form of the quadratic form $f\left(...
1
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0answers
34 views

How to make DSolve express constants in terms of the unknown function [closed]

If I do DSolve[y'[x] == y[x], y[x], x] Mathematica returns {{y[x] -> E^x C[1]}} Is there a way to have it return this ...
-1
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1answer
95 views

whether the real number $\theta$ exists or not

I want to find the real number $\theta$, which satisfies the following two equations: $$a_{11}+a_{12}\cos{(\pi/3)}=b_{11}\cos{\theta}+b_{12}\cos{(\theta+\pi/3)}$$ $$a_{12}\sin{(\pi/3)}=b_{11}\sin{\...

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