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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4
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0answers
34 views

Is there a name for systems of equations with min and max functions included?

In a big project I'm working on, I'm running into systems of equations that look like the following: $$a = \min(b, c)$$ $$b = d^2 + a$$ $$c = \max(a + b, d)$$ Basically, nonlinear systems of ...
0
votes
1answer
53 views

Simplifying a coupled-pendulum equation by assumption

I have been given the following question and I am unsure if I am missing an assumption or if I am misunderstanding something else: Two identitical pendula each of length $\ell$ and with bobs of ...
4
votes
1answer
82 views

Analyzing a linear system of equations from fMRI-data and extracting stimuli information

this is my first question in here and I hope I'll do it according to your expectations and rules and just start right now ;). At first I have to say that I'm not a mathematican so maybe I'm not ...
2
votes
2answers
168 views

How to find fixed point

I have recurrence equations of \begin{align*} x_{n+1} &:= 0.5\cdot (x_{n}^2+2\cdot y_{n}-2\cdot x_{n}\cdot y_{n}-2\cdot y_{n}^2) \\ y_{n+1} &:= -0.8\cdot (x_{n}^2+2\cdot y_{n}-2\cdot ...
0
votes
0answers
50 views

Iteration to Solve Unit Row Diagonally Dominant System

Given a matrix is unit row diagonally dominant $a_{ii}=1>\sum^n_{j=1,j\neq i} |a_{ij}|, \hspace{4mm} 1 \leq i \leq n$, prove that the following iteration will solve $Ax=b$ in the limit. $for ...
3
votes
2answers
166 views

Arc length paramatrizations satisfy original system of differential equations?

Say we have a system of differential equations $$ \begin{cases} x'''(t)+f(t)x'(t)=0\\ y'''(t)+f(t)y'(t)=0 \end{cases} $$ on an interval $[a,b]$, along with the restriction that $$ x'(t)^2+y'(t)^2=1 $$ ...
7
votes
2answers
117 views

Very simple partial differential equation

I am solving $$ \frac {\partial f}{\partial x} = \frac y{x^2 + y^2} \\ \frac {\partial f}{\partial y} = \frac {-x}{x^2 +y^2} $$ As $y$ was held constant when the partial derivative with respect to ...
1
vote
2answers
81 views

Why can't you swap rows in the matrix for a system of linear differential equations?

If you are given a Matrix A, and then asked to solve the initial value problem x'=Ax, why can one not swap rows before starting the problem. I tried it with a 3x3 matrix on wolfram alpha and got two ...
1
vote
1answer
62 views

Solution trajectories of a plane autonomous system

I have the plane autonomous system $\dfrac{dx}{dt}=x(1-2x-y)$ $\dfrac{dy}{dt}=y(1-x-2y)$ I need to show that the axes of the phase plane and the line $x=y$ are solution trajectories, but I don't ...
3
votes
3answers
79 views

Am I solving the system of differential equations the right way?

I have the following equations: $$ y_1'(t)=4y_1(t)-y_2(t)+f_1(t) $$ $$ y_2'(t)=2y_1(t)+2y_2(t)+f_2(t) $$ where: $$f_1(t)=\frac{e^{4t}\cos{t}}{e^{2t}+1}$$ ...
0
votes
0answers
52 views

When the system of equations below had a solution?

The system of equations is $$\begin{cases} \frac{c_1}{1-x_1}+\frac{c_2}{1-x_2}+\frac{c_3}{1-x_3}=0\\ \frac{c_1}{k-x_1}+\frac{c_2}{k-x_2}+\frac{c_3}{k-x_3}=0\\ ...
1
vote
1answer
121 views

I wonder whether the system of equations and inequations below have a solution.

I wonder whether the system of equations and inequations below have a solution. If there are solutions, what are they? A numerical solution is also desired. $$\begin{cases} ...
0
votes
2answers
1k views

How to solve Ax=0.. with 4 unknowns and 4 linear equations

I am trying to solve 4 linear equations for a 3D triangulation problem to create a function in matlab code. I have 4 equations such as aX + bY + cZ + dW = 0 eX + fY + gZ + hW = 0 iX + jY + kZ + lW ...
1
vote
1answer
79 views

Solve …

This is what I did Can anyone tell me what's wrong me or the question?
0
votes
1answer
27 views

System of ODE's of rational form

I am faced with a system of differential equations of the form $$ \begin{align} f'(x) &= \frac{\sum_i{p_i(x,f(x),g(x))\mathrm{e}^{i f(x)}}}{\sum_j{q_j(x,f(x),g(x))\mathrm{e}^{j f(x)}}} \\\ g'(x) ...
0
votes
1answer
26 views

how did they get equilibrium points from this answer?

could someone please show me how they got these equilibrium points? not sure if its just simple algebra or you have to do a derivative...how did they get equilibrium points from this answer? ...
1
vote
0answers
56 views

how to solve these kind of systems $x^2+y^2=z^2; z-y^3=5; xy=z$

Three variable system of equations with three variable with exponents for example $x^2+y^2=z^2$ $z-y^3=5$ $xz=y$
5
votes
1answer
82 views

For a system of PDEs, how many equations are needed generally for the system to have unique solution?

For an algebraic system of equations or a system of ordinary differential equations the following rule holds:(right?) the total number of unknown variables must be equal to the number of equations ...
7
votes
1answer
181 views

infinite matrix leading eigenvalue problem

I'm trying to find the leading eigenvalue and corresponding left and right eigenvectors of the following infinite matrix, for $\lambda>0$: $$ \mathrm{A}=\left( \begin{array}{cccccc} 1 ...
1
vote
0answers
22 views

Find a maximal set of independent equations in a system of non-linear equations.

Given a system of non-linear algebraic equations. Is there some general method to find a maximal set of independent equations in this system? For example, $\{x^2+y^2=1, x = y\}$ is a maximal set of ...
1
vote
1answer
931 views

Solving Linear Systems with Arbitrary Constants

I've run into somewhat of a problem during my Linear Algebra homework and I can't make heads or tails of it for some odd reason. I'm hopeful that one of you could help me out. It's worded as so : ...
0
votes
1answer
42 views

Solving a system of equations with summation

How to solve these equations with respect to $x$ and $y$: $$\underset{i=1}{\overset{n}{ \sum }}\left(b_i \left(a_i+b_ix+c_i y\right)\right)=0\land \underset{i=1}{\overset{n}{ \sum }}\left(c_i ...
0
votes
0answers
81 views

Particular Solutions and Green's Matrix

Find the particular solution which vanishes at $t=0$ and identify the Green's Matrix $G_0(t,s)$ $$x'_1=x_2+g_1(t), \\x'_2=-x_1+g_2(t)$$ This is half verification, half question on how to continue. ...
1
vote
1answer
35 views

Solving equations of the following form

I am currently studying resolution of concurrent forces and I have come across equations of the following type $$P\cos \theta+Q\sin \phi=C_1$$ $$P\sin \theta+Q\cos \phi=C_2$$ where $P$,$Q$,$C_1$and ...
0
votes
0answers
209 views

Kronecker-Capelli Theorem for system of congruences

Let $p$ be some prime. Given a system of linear congruences, \begin{align} m_1 x + n_1 y &\equiv c_1 \quad (mod\, p)\\ m_2 x + n_2 y &\equiv c_2 \quad (mod\,p)\\ \ldots \\ m_d x + n_d y ...
3
votes
1answer
36 views

Problem with system of equations

I wonder how to solve this system of equations: $\begin{cases} 2x^2+y^2=43\\2x^2+4xy=78\end{cases}$ when I subtract I have $y(4x-y)=35$ but I don't if it is good way to look for the solutions.
0
votes
0answers
16 views

Linear independent vectors and Base of linear Hull

Assignment Decide whether the following vectors are linear independent and give the Base of its linear Hull of the family $(v_i)_{i \in I}$: $$v_1 = \begin{pmatrix} 4 \\ 9 \\ 5 \end{pmatrix}, v_2 = ...
0
votes
3answers
42 views

Analytic solution to elliptic coupled ODEs

From my numerical solution I see that the solution to $$ \frac{dT}{dt} = a T - b h \\ \frac{dh}{dt} = -c h - d T $$ is an ellipse (where $a, b, c$ and $d$ are constants). Can this be solved ...
2
votes
1answer
49 views

How to solver this equation $\sum_{i=1}^{6}x_{i}x_j=-3,j=1,2,3,4,5,6,j\neq i$

Let $x_{i}\in R,i=1,2,3,4,5,6$ such that $$\begin{cases} x_{1}x_{2}+x_{1}x_{3}+x_{1}x_{4}+x_{1}x_{5}+x_{1}x_{6}=-3\\ x_{2}x_{1}+x_{2}x_{3}+x_{2}x_{4}+x_{2}x_{5}+x_{2}x_{6}=-3\\ ...
2
votes
1answer
69 views

Eigenvectors Trajectories

I got stuck with a problem while studying for a control systems exam. It goes as following: "Look at the picture of trajectories of a linear, time-invariant system with the form: ...
0
votes
0answers
35 views

Searching for a matrix that yields a nonnegative solution to a linear program

Suppose I have a system of linear equations $Az=b$, where $A$ has a Vandermonde structure of the form \begin{equation} A = \left(\begin{array}{cccc} 1 & 1 & \dots & 1 \\ x_1 & x_2 ...
4
votes
1answer
164 views

How to solve the six elements equations below?

How to get the exact or numerical solutions of the six elements equations below? $$\begin{cases} \frac{c_1}{1-x_1}+\frac{c_2}{1-x_2}+\frac{c_3}{1-x_3}=0\\ ...
3
votes
1answer
44 views

How to divide solutions of system of ODE

If I have the following system of ODEs: \begin{align} F'_1=aF_1+bF_2 \nonumber\\ F'_2=-bF_1+cF_2 \nonumber \end{align}for which I know the solutions of $F_1$ and $F_2$ as sums of exponential of ...
4
votes
0answers
90 views

if $(n+1)c_{n}=nc_{n-1}+2nd_{n-1},d_{n}=2c_{n-1}+d_{n-1}$How prove $c_{n},d_{n}$ are integers

let sequences $c_{n},d_{n}$ such $$c_{0}=0,d_{0}=1$$ and for $n\ge 1$,have $$c_{n}=\dfrac{n}{n+1}c_{n-1}+\dfrac{2n}{n+1}d_{n-1}$$ $$d_{n}=2c_{n-1}+d_{n-1}$$ show that $c_{n},d_{n}$ are integers. my ...
0
votes
2answers
57 views

Linear system of ODEs

Given is the ODE system $y'=\left(\begin{matrix}1\\1\\0\\ \end{matrix}\right)+\left(\begin{matrix}0&0&0\\0&k&0\\0&-k&k\\ \end{matrix} \right)y$ with boundary conditions ...
1
vote
2answers
65 views

Coupled differential equations method

$$\frac{dy}{dt} = (x-y)y$$ $$\frac{dx}{dt} = -y$$ How can I solve for $x(t), y(t)$? Is there a general method?
8
votes
5answers
279 views

Given $x+y$ and $x\cdot y$, what is $x^3+ y^3$ ?

I have been looking at an assortment of high school number sense tests and I noticed a reoccurring problem that states what x+y is and what $x\cdot y$ is then asks for $x^3+ y^3$. I want to know how ...
1
vote
2answers
56 views

Finding general solution for a nonhomogeneous system of equations

I have a system of differential equations: $\begin{cases} x_1'=x_2+2e^t \\ x_2'=x_1+t^2 \end{cases}$ And I want to find the general solution for it. I started by finding the general solution for the ...
1
vote
0answers
26 views

System of linear differential equations eigenproblem

In the Smith and Young 2001 paper on the Barotropic tide they have the governing equations... \begin{array}{rcl} u_t-f_0v+p_x & = & 0 \\v_t+f_0u+p_y & = & 0 \\p_z &= &b ...
0
votes
1answer
98 views

Plot of recurring system in MATLAB, Lozi map

I need to write this recurring system in MATLAB $$ x_{n+1}=1-a|x_n|+y_n$$ $$ y_{n+1}=bx_n $$ and take its plot for every $x_i,y_i$,with let's say a=1.4 and b=0.7. $$$$This is the Lozi map. And this ...
1
vote
1answer
54 views

System of equations with $n$ unknowns

How should I explain a $12$ year old that for solving a system of $n$ unknowns we need $n$ equations . I tried to show a example on a graph that for two variables we need two lines that intersect at a ...
2
votes
1answer
108 views

Solving a set of linear equations with a total of 35 variables

I have the following complex system of equations and I need to find a solution (or any possible number of solutions): c + d + g + j + n = 2000 b + e + g + k + o + u + w + y - J = 1500 a + e + h + l + ...
1
vote
3answers
85 views

$AX=B$ solve for $X$ … in MATRIX

$$ 2x - 3y + 4z = -19\\ 6x + 4y - 2z =8 \\ x + 5y + 4z = 23 $$ what I have done so far is I put the nubmer and $x, y $ and $ z$ in matrix form: $$ \begin{bmatrix} 2 & -3 & 4\\ ...
1
vote
1answer
70 views

Prove Gaussian Elimination Preserves this Matrix Property

Prove or disprove that if a matrix has the property $0 \neq |a_{ii}| \leq \sum_{\substack{j=1 \\j \neq i }}|a_{ij}|$ Then Gaussian elimination without pivoting will preserve this property I have ...
0
votes
3answers
38 views

Solving the following system of equation

I was trying to solve the following problem Find the extreme values of the function $$f(x,y)=2(x-y)^2-x^4-y^4$$ My attempt- $$p=\frac{\delta f}{\delta x}=4(x-x^3-y)$$ and $$q=\frac{\delta ...
2
votes
1answer
209 views

Gauss-Jordan Elimination to solve for variables

I have the following linear system: $$x + 2y - 3z = 4$$ $$3x - y + 5z = 2$$ $$4x + y + (s^2 - 14)z = s+2$$ Im trying to solve for $s$ to figure out how many solutions it has (if any). I know how to ...
2
votes
3answers
106 views

Solve this system by rewriting in row-echelon form $x+y+z=6$, $2x-y+z=3$, $3x-z=0$

This is my very first problem in Linear Algebra and I guess I really need to brush up on my Algebra skills..I'm at a loss as to how to solve this equation My reading said that there are basically 3 ...
0
votes
2answers
90 views

Number of real solutions for the following set of equations? [closed]

How to solve the following set of equations for real values of $x,y$ and $z$? $$x^2-y^2=z$$ $$y^2-z^2=x$$ $$z^2-x^2=y$$ $(0,0,0)$ is an obvious one solution.
0
votes
1answer
93 views

Solve a bit tricky system of equations

I want to solve the system for $x$, $y$ and $z$. Is there any smart trick to solve it? $$\begin{cases} 2a(ax+by)+2c(cx+dy)+2zx=0 \\ 2b(ax+by)+2d(cx+dy)+2zy=0 \\ x^2+y^2-1=0\end{cases}$$ $a,b,c,d \in ...
2
votes
0answers
50 views

How do I solve this question without solving for the functions?

The problem goes as follows: $$\begin{aligned} \frac{d y_1}{dt} &= -ay_1 \\ \frac{d y_2}{dt} &= -by_2 -\frac{dy_1}{dt} \\ y_1(0)&=M \\y_2(0)&=0 \end{aligned}$$ where ...