This tag indicates that several equations (of some type) must all hold. Do not use alone! Use in conjunction with (linear-algebra), (polynomials), (pde), (differential-equations), (inequalities) or another tag that describes the nature of the equations being considered.

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18 views

Coupled system of second order differential equations with variable coefficients

I am currently trying to find the solutions $\phi_1$ and $\phi_2$ of a system of coupled second order differential equations of the following form: $$ a(x)\phi_1''(x)+b(x)\phi_1'(x)+c(x)\phi_1(x)+d(x)\...
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1answer
58 views

solve two-dimensional nonlinear system numerically

Given the system $$x' = x(1 − y^2) \\ y' = y^2(1 − x^2)$$ I can plot the trajectories according to the analysis of its fixed points, but I need help with solving it numerically. Can anyone help me ...
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1answer
28 views

How can we find the possible values of 'a' in a system of linear equestion?

What is/are the possible value(s) of 'a' such that the system of linear equestion in x,y and z has a unique solution? ...
3
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1answer
28 views

Grade 10 system of linear equation problem

A farmer harvested $1$ section (which is $640\, acres$) of wheat and $2$ sections of barley. The total yield of grain for both areas was $99,840\, bushels$. The wheat sold for $6.35\, /bushel$ The ...
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1answer
150 views

MATLAB fsolve giving wrong solution

I tried to solve equations of 3 spheres using MATLAB's fsolve function, but it is giving the wrong solution. here is my MATLAB function ...
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1answer
32 views

How to resolve a set of equations when everything is cross related

First off mathematics isn't my field, so if I've made any rookie mistakes please forgive me! (also I'm not sure what tags to use) I have a set of equations that boil down to this; $s = \int Vdt$ $V ...
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1answer
23 views

Can this system of equations be solved exactly?

I have a problem which I have been able to reduce to the following vector equation: $2 \alpha \vec{f} [C_0 + C_T \ \vec{a}.\vec{f}] = - C_T \ \vec{a}$ where $\alpha, C_0$ and $ C_T$ are all ...
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0answers
13 views

Linear equalities and nonequalities over finite group

Would anyone know where I could find more information on counting the number of solutions to a system of equations involving linear equalities and nonequalities over a finite group? For example, let $...
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2answers
50 views

How can we solve the linear system? [closed]

How can we solve the following linear system ? $$ax+by=0 \\ cx+dy\neq 0$$
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1answer
33 views

Draw phase portrait of this system

Consider the system: $$ \begin{cases} x'=xy\\ y'= -x^2. \end{cases} $$ I find that for this system, the line $x=0$ are a line of fixed points. I wonder how to draw the phase portrait for this system.
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1answer
26 views

Give the general solution of the $2\times 2$ inhomogeneous system of differential equations

Give the general solution of the system: $$X'(t) = \begin{pmatrix} 3 & 1 \\ 1 & 3 \end{pmatrix} X(t)+\begin{pmatrix} 2e^{2t} \\ 0 \end{pmatrix} $$ I manage to come to the general solution to ...
2
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2answers
48 views

Prove that $\alpha=\beta=\gamma$

Q. Let $x,y,z \in \Bbb R-\{0\}$ and $\alpha,\beta,\gamma \in \Bbb C$ such that $|\alpha|=|\beta|=|\gamma|=1$. If $x+y+z=0=\alpha x+\beta y+\gamma z$, then prove that $\alpha=\beta=\gamma$. My ...
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1answer
62 views

System of differential equations: where did I got wrong?

I have the system: $$x_1'=2x_1-x_2+e^{2t}\\ x_2'=4x_1+2x_2+4$$ So I searched for the homogeneous solutions and got: $$X_H=c_1e^{2t} \left(\begin{matrix} \cos 2t \\ 2\sin ...
1
vote
1answer
40 views

Why equations are called independent and dependent?

I am not sure if I am trying to know everything to detail, but why for example two equations are called independent if they have only single solution? On what they think about when they say single ...
0
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1answer
65 views

System of differential equations

We suppose that we have a system of differential equations $$\left\{\begin{matrix} L_1 y=0\\ L_2 y=0 \end{matrix}\right. \tag 1$$ where there order of $L_1 y$ is $n$ and the order of $L_2 y$ is $m$...
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1answer
14 views

Find the equation of the line for this impilcit differential

Here is the question. A set of points in this graph that satisfies the the equation of the line tangent to this curve at the point (0,4) So I started by finding the derivative But I am not ...
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1answer
35 views

Solving a nonlinear algebraic system representing the equilibrium of a system of ODEs

Given the following system: $$ a_1+(a_3+a_4)V-a_5WX = 0 \\ (a_7+a_4)Y-a_6WZ = 0 \\ a_2-W(a_4+a_5X+a_6Z)+(a_3+a_8)V+a_7Y = 0 \\ a_5WX-(a_3+a_8+a_4)V = 0 \\ a_6WZ-(a_7+a_4)Y = 0 $$ where $a_1$ to $a_8$...
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0answers
27 views

Questions regarding the basis for the solution set of a system.

I've seen a couple of examples like this but there's a thing I don't understand. I have to determine a basis for the solution set of the system: $$x-y-7=0\\ 2x-y+7=0$$ So based on the examples, ...
1
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1answer
50 views

The Rank of the Matrix Given its Solution Space

$\quad$ Let $A$ be a $5$x$4$ matrix.There exists a vector(column) $B=[0,1,2,3,4]^{T}$ such that the solution space of $AX=B$ is $[1+2s,2+3s,3+4s,4+5s]^{T}$where $s \in \mathbb R$. Find the rank of the ...
2
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1answer
54 views

Possible values of $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$ given $x+y+z=1$

Given $x,y,z$ are real numbers and $x+y+z=1$ and $x$ is not equal to $z$, if $ {1\over x} + {1\over y} + {1\over z} = m $, which of the following values of $m$ are possible? (A) 1 (B) 2 (C) 3 (D)...
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2answers
43 views

Solving Currents in Electrical Networks for Graph Theory

I need help trying to solve this question, been cracking my head for the whole week and my professor said he used an online solver but in exams we have to solve by hand! Given these 8 equations, we ...
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3answers
44 views

System of equations based question in matrix form

If $\begin{bmatrix}1^2&2^2&3^2\\2^2&3^2&4^2\\3^2&4^2&5^2\\4^2&5^2&6^2\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}1\\4\\10\\\lambda\end{bmatrix}$,...
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1answer
21 views

Number of solutions in a system for values a and b

In general, if you are given a system with some a and b like $x + y + z = a $ $x + 2z= b$ $x + ay + z=b$ And asked to find the values a and b such that the system has no solution, infinitely many ...
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1answer
20 views

Square of a matrix as coefficients for a system of linear equations

small question I'm having a disagreement with a classmate over - it's a question in a book: Let $A$ be a square matrix $n \times n$ Prove or disprove: If the system $A\underline{x}=\underline{b}$ ...
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2answers
58 views

How to solve system: x_1+x_2+…+x_n=a [closed]

How to solve this system: $$\left\{\begin{matrix} x_1 & + &x_2 & + & \ldots & + & x_n &= & a \\ x^2_1& + &x^2_2 &+ & \ldots & + &x^2_n &=...
4
votes
2answers
127 views

Solving sub-matrix preserving overall linear system

I have a linear system $$ \begin{pmatrix} A_{11} \ A_{12} \ A_{13}\\ A_{21} \ A_{22} \ A_{23}\\ A_{31} \ A_{32} \ A_{33}\\ \end{pmatrix} \cdot \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \begin{...
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1answer
37 views

System of n equations

I had a task which was solved (here you can find it: System of two equations with two different non-linear variables). I looked at it wider and I'm wondering now what if there would be system of $n$ ...
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1answer
27 views

How to show a certain integer solution does not exist for a system of linear equations?

I'm having some trouble with the following problem: Considering an independent system of linear equations in $x$ and $y$ with integer coefficients \begin{equation} ax + by = c_1\\ cx + dy = c_2. \end{...
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0answers
45 views

Differential Equations on Population

I've been beginning to try to solve some simple differential equations. I reached a problem where there is a polar bear population $p(t)$ and a seal population $s(t)$ that are governed by $$\frac{dp}{...
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2answers
53 views

System of two equations with two different non-linear variables

I have to solve this system of equations for real $x$ and $y$: $2x^3+4=x^2(y+3)$ $2y^3+4=y^2(x+3)$ I noticed that they are symetric and, assuming that $x=y$, I got two solutions: $x=y=-1$ or $x=y=2$...
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0answers
166 views

About solving a system of first order ODEs with non constant coefficients

I'm trying to solve this system of ODEs \begin{align*} &S'(t)=-\lambda(t)S(t)+{\tau}R(t)\\ &I'(t)=\lambda(t)S(t)-{\gamma}I(t)+r(t)L(t)\\ &R'(t)=(1-q){\gamma}I(t)-{\tau}R(t)\\ &L'(t)=q{...
2
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1answer
194 views

Help with using the Runge-Kutta 4th order method on a system of three first order ODE's.

The original ODE I had was $4f‴ + ff″ + 2(f′)² = 0$ with $f(0)=0, f′(0)=0$ & $f′(∞)=0$ I wish to use the 4th order Runge-Kutta method, so I have the system of three 1st order equation as below: ...
2
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2answers
46 views

Is it possible to find solution of this system of equations?

Following is augmented matrix which has been reduced to row echelon form by using row operations. So when I convert it to system of equations I would get 3 ...
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0answers
33 views

Implicit function theorem: Lower bound on radius

Let $f: \mathbb{R} \times \mathbb{R}^n \to \mathbb{R}$ be sufficiently smooth with $f(x_0,y_0) = 0$ and the Jacobian $J_yf(x_0,y_0)$ of $f$ with respect to the second variable $y$ is invertible at a ...
2
votes
2answers
34 views

Simultaneous equations

How can I find the solution $(3, 3, \frac{-3}{2})$ from the following system of equations: $x+(y-1) z = 0$ $(x-1) z+y = 0$ $x (y-1)-y+2 z = 0$ I have done eq1 - eq2 to find the other solutions. ...
0
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1answer
52 views

Solve the following relation.

Find the values for $a$, $b$, $c$ and $d$ in the following equation $$\frac{2a}{2m} = \frac{2b}{a+m} = \frac{2c}{a+b} = \frac{2d}{c+m} = \frac{2M}{c+d}.$$ (Note: $m$ and $M$ are different. In fact, $...
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2answers
20 views

Intersection beween circle and line

So I have the circl $x^2+y^2=5$ and the line $y=2x+c$ and I want to find all the points were the two intersect. I know how to solve this for a specific value of $c$, but I do not know how to handle ...
0
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1answer
22 views

Solve the following system of equations for a,b and c

$ax+bx^{-1}+cx^3 = 0 \ (1) $ $a - bx^{-2} + 3cx^2 = 0 \ (2)$ $bx^{-3} + 6cx = x\cos x \ (3)$ If the coefficients were constants I would have used matrix row operations however this is not the case.
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1answer
170 views

Solutions of $x^p+y^q=y^r+z^p=z^q+x^r$

I'm struggling with the following problem from Terence Tao's "Solving Mathematical Problems": Find all positive reals $x,y,z$ and all positive integers $p,q,r$ such that $$x^p+y^q=y^r+z^p=z^q+x^...
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2answers
48 views

How to solve this equation with three variables arithmetically?

How can we find the sum of $x$, $y$, and $z$ arithmetically? $$x+y=6$$ $$z+y=10$$ $$x+y+z=?$$ Some things I have tried: $$y=6-x$$ $$y=10-z$$ $$6-x=10-z$$ $$z-x=4$$ or $$x+2y+z=16$$ or $$x=6-y$$ $$z=...
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1answer
37 views

Systems of first order linear ODE

Consider vectors $$ x^{(1)}(t) = \left( \begin{array}{cccc} t \\ 1 \\ \end{array} \right) \ $$ $$ x^{(2)}(t) = \left( \begin{array}{cccc} e^t \\ e^t \\ \end{array} \right) \ $$ (a) Compute the ...
3
votes
1answer
35 views

How are theses functions called and what are their properties?

We define a system of two equations with two variables and six parameters: $\begin{cases} a_1x+b_1y=c_1\\ a_2x+b_2y=c_2 \end{cases}$ We obtain a function $f:\mathbb{R^3\times\mathbb{R}^2\rightarrow\...
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1answer
30 views

Issue with a formal notation.

I was thinking how to formally express a set of the following property. First of all we have got a set of $i\in\{a,b,c,...\}$. Then we want to consider equations of an arbitrary form (say: $x_i\leq i'$...
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2answers
18 views

Alternative solution for the following equation

$$x^2+x+3=0$$ Solve it in $$ \Bbb Z_{22} $$ Does there exist another method of solving this equation,besides making a table to calculate all the possibilities. Note that $$ 3,0 ∈\Bbb Z_{22} $$
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0answers
28 views

Why is the *least-norm* solution useful or desirable?

For a problem at work, I had to write a program that would solve a system of linear equations. Often times the problem would lead to an underdetermined system (where there are less equations than ...
0
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1answer
31 views

How to solve system of congruence modulo equations?

So I have these two congruence equations, and I need to solve for x and y (or determine that it is unsolvable). I have been searching for hours and can't figure out how to solve this, or how to even ...
1
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1answer
56 views

Solve for real $x$ and $y$

$$x^4+2x^3-y=-\frac{1}{4}+\sqrt3$$$$y^4+2y^3-x=-\frac{1}{4}-\sqrt3$$ I know this problem has something which I am missing(no one's making a 16 degree equation). It probably has some common factor or ...
0
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0answers
49 views

Numerics: Solving inhomogeneous Helmholtz equation

My mathematical english is not the best, so I hope you gonna understand my translation of the issue I'm trying to solve. Sorry, I don't know either how to use MathJax. The problem is a lack of basic ...
1
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3answers
33 views

How many solutions this a multidimensional system have?

How many solutions have this system of equations: \begin{array}{l} \ 3x^2+y+2xy^2-3 = 0 \\ \ x + 2yx = 0 \end{array} The more general case is when we want to solve two nonlinear algebraic equations ...
0
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2answers
48 views

Does this linear system have no solutions?

Am I correct in saying if I have a linear system where a variable equals two different outputs, then there are no solutions? E.g., $$\begin{cases}x= 4 \\ x=5\end{cases}$$