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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Solving a complex equation analytically

In my attempt to find a solution to my own question over at CrossValidated, I want to solve the following equation for $p$: $t^2=p^2\left[1 - \frac{m}{p}Y-Y^2\right]$ where $Y=\frac{\frac{1}{\sqrt{2\...
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1answer
83 views

Find centre of spiral similarity of two lines

I am trying to find a formula for the centre of spiral similarity (see here) of two lines, lineAB and lineCD. My problem comes ...
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42 views

How can I know what is # in equation? [duplicate]

I am trying to find the solution by using Reduce to fit my data with FindFit. And I don't know what ...
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1answer
34 views

Solve multiple equations with a parameter by means of Reduce

I have developed a program that solves an equation and give its solutions as outputs: ...
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1answer
62 views

Avoiding/skipping singularity error in ParametricNDSolve

I've looked up a few examples of similar errors for ODE's with singular points, but have yet to figure out a way to solve this problem for my case. A simple patch up where the singular point is '...
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1answer
81 views

Plot the phase portrait of a differential equation by using StreamPlot

How can I plot phase portrait by using different initial conditions? Are these conditions already specified when I choose the min and max values in the StreamPlot command? I will post the equation ...
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3answers
202 views

How to Solve Functional Differential Equation

I tried to solve this equation numerically. eqnEx = x''[t] + x[2 t] == 0; NDSolve[{eqnEx, x[1] == 10, x'[1] == 0}, x[t], {t, 1, 10}] Two important character of the ...
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Compile and NSolve

Consider the following numerical problem. One deals with transcendental complicated function f that depends on several parameters and three variables, say ...
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32 views

Solving for a few roots in the neighborhood of an initial point for an eigen-equation with many roots

I have a system that is described by a complex matrix, $U$, which is a function of two parameters $f, \beta$ (a dispersion eigen-relation in wave physics). We are interested in the solutions ($f,\beta$...
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1answer
63 views

How to solve integro-differential with parameters iteratively?

I am trying to solve an integro-differential equation and tried using one of the answers that I found in a related question: Numerically solve an integro-differential equation The difference is I have ...
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3answers
203 views

Finding the enclosed area between two equations

I have to find the sum of the enclosed area between two functions that goes from 0 to 2pi: ...
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48 views

Strange behavior of FindInstance

I try to solve a problem from Kazakhstan math school competition (see it here in Russian) by ...
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1answer
66 views

How does Mathematica solve this system of nonlinear equations?

During a calculation for a physics lab, I ran into the following six non-linear equations with unknowns $x_1,x_2,x_3,x_4,x_5,x_6 \in \mathbb{R}$ ...
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1answer
69 views

How to get Sum of array of integers?

This question seems easy but I am struggling with it now, I tried a few ways and check this solution as well but couldn't help me, please check and help if you are able: So I need to save the sum of ...
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47 views

How to simplify sqrt without imaginary unit

I've a system of equations and one solution that Mathematica throws is: $$ x=\frac{\mathbb{I} b \sqrt{pA - pS}}{\sqrt{-3 pA + 3 pS}}$$ knowing that $pS,pA \in \mathbb{R}$ and allways $$ pS > pA $$ ...
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1answer
26 views

Using Simplify and Reduce with Assumptions when the inequality is already one of the assumptions

I am using the Simplify and Reduce functions to reduce inequalities, but somehow the function Simplify does not consistently give "True" when the inequality happens to be one of the ...
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How to solve a system with infinitely many equations?

I need to solve the following system of (infinitely many) equations. I am looking for $V(0,0)$ $t \in \{0,1,2.....\}$ with one caveat that $s \leq 1+t$ should hold. $ s \in \{1,2,3,L-1\}$ fixed ...
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3answers
87 views

Findroot and plot not showing line

I need help solving this equation $$2- 12 sin(3 x) - 6 x = 0$$ using FindRoot, but it does not seem to work. For example, ...
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0answers
59 views

how can I get an expression in the form of another expression

I need help solving this equation, I have done it by hand, but it is not very efficient to do. Express |z-i|=2|z+1| in the form |z+a|=b, where z ∈ C and a ∈ C and b ∈ R+ I used this: ...
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1answer
74 views

Modelling transparent boundary conditions on a three-bonded quantum graph

I've created two issue last year, but unfortunately was able to return to this problem only now. This question is a continue to this issue. Essentially I am now trying to apply a solution from the ...
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1answer
345 views

Some doubts about symbolic equations in Wolfram Mathematica

I need to perform the following operations using Wolfram Mathematica. I have these equations: $$a b = c+d+e$$ $$\frac{d}{f}=g h + i$$ $$k=\frac{a}{c}$$ I need to obtain $k$ as a function of: $a,b,c,e,...
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1answer
43 views

Partial derivative on a Solve solution

Trying to solve a demand-supply equilibrium here and them find a partial derivative of the equilibrium with respect to the parameters. ...
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1answer
95 views

Getting Mathematica to solve a system of two second order nonlinear ordinary differential equations

I tried solving a system of two second order nonlinear ordinary differential equations using the DSolve command. First, I tried like this: ...
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1answer
52 views

Using a Groebner Basis to show Bijectivity

I have a set of n polynomials over n variables, like ...
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1answer
54 views

Why does Reduce give False on SameQ with its copy-pasted result?

If I evaluate Reduce[#, x] & /@ {{4 x > 1, 2 x < 5}, {5 x > 1, x < 5}, {4 x > 1, x < 5}} the result is ...
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1answer
55 views

Does FindInstance traverse the entire domain?

If the result of FindInstance[expr<=0,vars,dom] is empty set, can it mean that expr is always greater than ...
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1answer
108 views

Square root problem

Consider the following code NDSolveValue[{ x'[t] == x[t]^a, x[0] == 0 }, x, {t, 0, 10}] which solves the equation $x'(t)=x(t)^a$, for some exponent $a$, with ...
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1answer
75 views

Optimization of second order ODE with more than one parameter

I want to optimize a second order ODE with more than one variable: ...
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43 views

Solve a system of algebraic equations

I'd like to determine whether there exist $\beta>0$, $A_i(i=1,\cdots,5)$, $B_i(i=1,\cdots,4)$, $C_i(i=1,\cdots,3)$, $D_i(i=1,2)$, and $G_1\in\mathbb{R}$,such that these parameters satisfy the ...
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1answer
30 views

testing linear independence for an unknown number of matrices

I would like to test if 16 matrices (4X4) that I created are linearly independent. The straight-forward solution would be to check if the equation $\sum_{k=1}^N \alpha_k A_k = 0$ (1) (N=16 in the ...
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1answer
59 views

Solving an equation, and verifying that it is correct

I want to solve the equation Solve[e == 1/2 (-2 ef + hvk - Sqrt[9 hvk^2 + 4 j^2]), hvk] I then obtain the solutions ...
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1answer
55 views

Is it possible to ask Mathematica to give all the roots of the given function?

I have this equation $$ 36 \cos \frac{3 x}{4} \cos \frac{27 x}{20} \left(\cos \frac{3 x}{5} +2 \cos \frac{21 x}{10} \right)=0 $$ Is it possible to ask Mathematica to give all the roots of the ...
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68 views

Can Mathematica solve this exponential equation

My version (12.1.0.0 Student Edition) does not solve this equation: Solve[Exp [-n^2/(2 m)] <= 3/4, m] WolframAlpha finds the solutions, but only for integer n? ...
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Hi. I'm a beginner so I need help to solve this equations using Regula-Falsi to find root of the equation (which is x)

I've been trying to look for an example but only with one unknown. In my case of studies, I have 4 unknowns. I just want to make sure is it correct the way I'm writing the coding to find the root ...
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How to solve this inequality with Reduce or Solve?

I need to solve this inequality: ...
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36 views

How to prove that this function has a unique root? [migrated]

I want to show that f has always a unique root, ...
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1answer
47 views

solving differential equation with matrices

I have to solve two coupled differential equations: ...
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2answers
85 views

Computing periodic points of some function

Given a function h[{x_, y_}, b_, c_] := {x^2 + c - b*y, x} for some parameter values b and c ...
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3answers
85 views

ODE problem using DSolve

I would like to use DSolve (or NDSolve) to verify that the solution to the ODE problem -4(v''[t]+(2/t)v'[t])-2*v[t]*Log[v[t]]-(3+(3/2)Log[4 Pi])*v[t]==0, for $t\...
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1answer
47 views

Solving abstract factorization problem with Mathematica

I'm a Mathematica newbie. Given something like: $$(r_0 + r_1 a + r_2 a^2 + r_3 a^5)(r'_0 + r'_1b + r'_2 b^2 + r'_3 b^5) = 1 - a^5 b^5$$ I'd like to determine if there exist $r_i,r'_i$ that solve the ...
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1answer
87 views

Solving an ordinary differential equation with boundary condition at infinity

I want to solve the following differential equation f''[z] + (1/z)*f'[z] - f[z] + f[z]^3 == 0 subject to the boundary conditions $$f^{\prime}(0)=0\qquad\lim_{z\to\...
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31 views

can not replace when use ctrl+f

I have a very long output, therefore, I want to find and replace some repeated expressions with abbreviations using crtl +f in Mathematica. when I enter expressions, the mathematical can find it and ...
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1answer
53 views

Numeric solution of ODEs oscillates strongly and stops halfway?

I tried to reproduce the results of a paper. The differential equations are given by ...
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1answer
46 views

NSolve missing solutions

I'm having trouble solving the transcendental equation. For some values ​​of bi, NSolve obtains 6 roots, however when changing the value, it obtains 5. Graphing the function clearly shows that the ...
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0answers
48 views

Why doesn't Reduce work?

I try to solve an inequality with parameters using Reduce. The answer i get is : This system cannot be solved with the methods available to Reduce. Here is the inequality: ...
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2answers
76 views

Forcing mathematica to solve polynomials exactly

It used to be the default behavior that Mathematica would solve polynomials of degree 4 exactly. In the current version I have (12.2.2.0) it sometimes gives numerical answers. Is there a way to change ...
3
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1answer
63 views

Solve yields complex Root even if the domain is Reals

I want to solve $x^3=a^2$ for $x$ where $a>0$ and $x$ is real. The answer I want is $$x=a^{2/3}.$$ On Wolfram Cloud, I tried ...
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1answer
41 views

Numerically obtaining roots as a function of another variable

I have an equation $f(x,y) =0$ that Mathematica can solve numerically using NSolve for a fixed $y$. I want to perform the following operation: ...
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0answers
32 views

Solve coupled equations in the steady state

I want to solve 16 coupled differential equations in the steady state. Among the answers, I only require two of the answers. But the Mathematica does not show me the answers in detail!!! Can anybody ...
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1answer
62 views

Solve equation system for expression [closed]

How to solve this equations and find specified expression (all integers)? x * N + y = 2012 y * N + x = 2011 x + y = ? I've tried but got formulas as an answer ...

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