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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1answer
35 views

Show that the solution of the differential system are periodic.

Let $y,z$ two functions defined on $\mathbb{R}$. Show that the solution of the differential system : $$ y'=z^3 \qquad z'=-y^3 $$ are periodic. My attempt : With some works I can show that ...
2
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1answer
54 views

Is it possible for a system of equations to have a non-zero determinant and no solution at the same time?

I am quite confused by the solution I was given for the following problems: a) Solve the following system of equations using Gauss elimination only: $2x - y = 5$ $-x + 2y = -4$ $3x - y = -1$ b) ...
0
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1answer
61 views

Solve the recurrence relation $f(n) = f(n - 1) + f(n - 2) + f(n - 3)$

This is a problem I was playing with that troubled me greatly. $f(n) = f(n - 1) + f(n - 2) + f(n - 3)$ $f(1) = f(2) = 1$ $f(3) = 2$ So, the goal is to try and find a solution for f(n). I tried ...
2
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1answer
60 views

Method of characteristics for a system of pdes

I can do parts a) and b) as follows $\begin{pmatrix} 1&0&0 \\ 0&1&0 \\ 0&0&1\end{pmatrix}\frac{\partial}{\partial{}x}\begin{pmatrix} u \\ v \\ w\end{pmatrix}+\begin{pmatrix} ...
1
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1answer
39 views

PRobability Markov chain, system of equations

I'm looking for techniques or tricks to solve a system of linear equations you get where you want to find the limiting probabilities. The system is this: $\pi_0 = 0.7\pi_0 + 0.2\pi_1 + 0.1\pi_2$ ( ...
4
votes
2answers
55 views

Solve numerical system of nonlinear equations?

I need to solve a nonlinear system of equations that looks like this ...
0
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1answer
47 views

System of equations with a unique solution, no solution or an infinite number of solutions

I was doing a past OCR Further Pure 1 Paper from January 2011, but came across the following question that I could not solve, even with the help of the mark scheme: Determine whether the ...
0
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0answers
31 views

a system of linear equations $x-y+z=0$

Yall are probably gonna think me a noob. But I am working on this eigenvector problem and I reduced the matrix to $x-y+z=0$ . How do I describe this solution set. I know how to do it if it's just ...
0
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1answer
31 views

Using Laplace Transform to solve a 3 by 3 system of differential equations

I have been trying to solve this system of equations using Laplace transforms for a while. It is very easy to solve it using eigenvalues and eigenvectors, but when I tried to do it using Laplace I ...
0
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0answers
10 views

Finding an isometry in high dimension

Given two points $x,y \in \mathbb{R}^D$, I am looking for the isometry $A\in \mathbb{R}^{D\times D}$ that maps $x$ to $y$: $Ax=y$ I want to determine the $D^2$ parameters constituting $A$. When is ...
0
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1answer
36 views

Finding equations when given new center of a circle

$y = −x + \sqrt{2}$, $y = −x − \sqrt{2}$, $y = x + \sqrt{2}$, and $y = x − \sqrt{2}$. These equations determine lines, which in turn bound a diamond shaped region in the plane. Construct a diamond ...
4
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2answers
118 views

A calculus problem with functions such that $f''(x) = g(x)$ and $g''(x) = f(x)$

Let: $f(x)$ and $g(x)$ be twice differentiable, non-decreasing functions. $f''(x) = g(x)$ and $g''(x) = f(x)$. $f(x) \cdot g(x)$ is a linear function. Then we have to show that $f(x) = g(x) = ...
1
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3answers
71 views

How do we know that if $Ax = b$ has a unique solution, $A$ is invertible?

We are of course assuming $A$ is an $n\times n$ matrix. I know there's a proof of it going the other way (invertibility implies a unique solution), but I'm trying to work out a proof going this way. ...
0
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1answer
70 views

Math Constraint Problems

This is a homework problem of mine. The professor said we can use any resource to help us solve and I cannot get up with anyone from class. Please help. I'm not looking for a direct answer, I ...
1
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1answer
27 views

Finite differences coefficients

I'm interested in deriving a forward finite difference approximation for the gradient of a function, $f(x)$, at the point $x = x_i$ using $k+1$ points. If the spatial domain is uniformly discretized, ...
1
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2answers
34 views

Systems of equations by substitution help

I'm trying to solve a systems of equations problem but I can't seem to see what I'm doing wrong... As far as I can tell the way to solve a system of equations by substitution involves the following ...
1
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1answer
37 views

solving a linearly-constrained sparse linear least-squares problem

Given the system of equations $Ax=b$, subject to $Cx\le d$ where $A$ is an $n\times m$ matrix (with $n>m$) and is very large and sparse. As an example $A$ can have $3126250\times 2740$ elements. ...
4
votes
1answer
67 views

Due to numerical inaccuracy, the solution of a boundary value problems becomes negative

I treat a toy example to get my point across. In reality I have to deal with a much more complex model. Let us consider a one dimensional boundary value problem using the bvp5c solver in Matlab. Two ...
0
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0answers
36 views

solving simple system of cubic equations

I know, that there is no general answer as how to solve a system of equations. But mine has a pretty special form. Let $x,a,b \in \mathbb{R}^n$ and $a,b$ are known. I want to find the solution of the ...
1
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0answers
48 views

Frobenius Method For System of Differential Equations

I have a system of ODEs. Can you explain how to solve a system of ODEs using the method Frobenius expansions ? There are 5 ODEs which are coupled and 5 variables. $\omega\hat\rho + i\alpha V_z ...
0
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2answers
34 views

Solvability of this linear equation system and finding particular solution/

I have been given a task, that involves determining if this lin.eq.system $$ x_1+2x_2-3x_3+10x_4-x_5=7\\x_1-2x_2+3x_3-10x_4+x_5=9\\x_1+6x_2-9x_3+30x_4-3x_5=5 $$ has a solution by using what our ...
0
votes
1answer
32 views

How to Split a 2D Gaussian pdf into a Grid of Equally Sized Volumes

Let $f(x,y)$ be a Gaussian pdf for some known mean and covariance. Given $(x_0, y_0)$ and $(x_N, y_M)$ such that $$\int_{x_0}^{x_N} \int_{y_0}^{y_M} f(x,y) dy dx \approx 1$$ I would like to split ...
0
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1answer
34 views

Difficult augmented matrices question.

I'm currently revising for a maths module that I am taking as part of my physics degree. The final part of the matrices section of a paper I was doing included this question: Solve the this set of ...
0
votes
1answer
47 views

FermiPasta-Ulam problem

Consider $H(q,p) = \frac{1}{2} \sum\limits_{j=1}^{n+1} {(p_j^2 + (q_{j}-q_{j-1})^2)}$ $H(q,p) $ is the Hamiltonian considered in the FermiPasta-Ulam problem. Consider canonical transformation $Q = ...
4
votes
4answers
95 views

Solve system of nonlinear equations using non-numerical method

Is there any non-numerical method to solve this kind of system of nonlinear equations for $c_1, c_2, x_1, x_2$: $$c_1+c_2 = 1$$ $$c_1x_1+c_2x_2 = 1$$ $$c_1x_1^2+c_2x_2^2 = 2$$ $$c_1x_1^3+c_2x_2^3 = ...
2
votes
3answers
54 views

Does adding two linear equations will result in a line which will pass through an intersection of the linear equations?

I was wondering why it is almost impossible to find a geometrical explanation of why adding two linear equations helps us to find a solution of a system of linear equations? Am I right that adding two ...
4
votes
2answers
40 views

Prove or disprove the system about $n$th power has only one solution $x=y=1$

$$\begin{cases}x^n+y^n=2\\x+y=2\end{cases}\;,\;n\in\mathbb{N}\;,\;x,y\in\mathbb{R}\;,\;n>2$$ I have tried to show that $\displaystyle y'=-\frac{x^{n-1}}{y^{n-1}}=-1$ $$......$$ therefore $x=y=1$ ...
1
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1answer
45 views

solving a non-linear (trigonometric) system of equations with two equations and two variables

I'm trying to solve the following system of equations: $$l_1*sin(\alpha)=l_2*cos(\gamma)+l_3*sin(\beta)$$ $$l_2*sin(\gamma)+l_1*cos(\alpha)=l_3*cos(\beta)+l_4$$ with the unknowns $\beta$, $\gamma$ ...
0
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0answers
22 views

Counting the roots of nonlinear systems of equations

I have a "nice" function (vector field) $$\mathbf{f}: \mathbb{R}^n \rightarrow \mathbb{R}^n$$ and I need to find how many roots (zeros) it has in a certain domain (hopefully prove that it has at most ...
0
votes
4answers
84 views

What am I doing wrong here?

Consider this system of equations: $$ \begin{cases} x+y=6\\x-y=5\\2x+3y=7 \end{cases} $$ This is an overdetermined system and doesn't have a solution (the 3 lines don't intersect). But by adding 2nd ...
1
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0answers
44 views

Phase portrait of DS with skew symmetric matrix

How should I draw phase portrait of DS: $x'=Ax$, where $$A=\left( \begin{array}{ccc} 0 & 1 & 0 \\ -1 & 0 & -2 \\ 0 & 2 & 0 \\ \end{array} \right)?$$ Eigenvalues here are $0, ...
1
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0answers
50 views

find $x$, given $\{c_ix = k_i + y_i\}_{i=[1,n]} $

Given $$c_1x = k_1 + y_1 $$ $$c_2x = k_2 + y_2 $$ $$\vdots $$ $$c_nx = k_n + y_n $$ where the values of $\{c_1 \ldots c_n \}$ and $\{ k_1 \ldots k_n \}$ are known, and $x, \{y_1 \ldots y_n \}$ are ...
5
votes
0answers
98 views

How to solve a particular initial-boundary value problem

I have the following initial-boundary value problem $$\begin{cases}\dfrac{\partial^2 u_1}{\partial x^2}=A_{11}\dfrac{\partial u_1}{\partial t}+A_{12}\dfrac{\partial u_2}{\partial ...
3
votes
0answers
47 views

Solving a system of 3 variables

How to solve or what is the algorithm to solve a system of equations like this: $$\eqalign{ (x +\phantom{3} z)^2 + (y +\phantom{3} w)^2 &= 52\cr (x + 3z)^2 + (y + 3w)^2 &= 296\cr (x ...
1
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1answer
39 views

How to solve system of nonlinear differeintial equations

System follows: $$ y'=\frac{y^2}{z-x}; z'=y+1$$ I was found the 2 ways. The both are wrong 1) $$z = x + \frac{y^2}{y'}; z'=1+\frac{2yy'^2-y^2y''}{y'^2}=y+1; => (p(y) = y')=> yp(yp'+p)=0;$$ ...
1
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2answers
70 views

System of Nonhomogeneous DEs - Help Solving???

I'm studying for finals at the moment and could use some help with solving the particular solution for this system of nonhomogeneous differential equations: $x' = \begin{bmatrix}1 & 0\\ 2 & ...
0
votes
1answer
14 views

How to Do Trilateration?

Trilateration is the process of calculating the coordinates of a point by using its distances to three other points. Say that, we have three points of which we know the coordinates: $A(A_x, A_y)$ ...
-1
votes
2answers
93 views

Solving the particular solution of system of nonhomogeneous DEs???

I am studying for finals at the moment, and I'm trying to better understand using the method of underdetermined coefficients to solve a system of DEs. Here's an example of one I'm stuck on at the ...
1
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1answer
11 views

Finding values $a$ and $b$ which transforms a differential equation

Given the function $u = u(\xi, \eta)$ where $\xi = x + ay$ and $\eta = x + by$, find the values of $a$ and $b$ such that they transform the equation $$\frac{\partial^{2}u}{\partial x^{2 }} + ...
1
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3answers
29 views

Why the linear numerator for fractions with irreducible denominators and constant numerators for reducible denominators? [duplicate]

For example: $\Large{\frac{2x^3+5x+1}{(x^2+4)(x^2+x+2)}}$ breaks down to $\Large{\frac{ax+b}{x^2+4}+\frac{cx+d}{x^2+x+2}}$ I have been told that since the denominators are irreducible, the ...
0
votes
0answers
14 views

Criterion of removal of equations from overdetermined system

Consider the problem of solving overdetermined system Ax = b; In the problem I am trying to solve (from the field of spectral unmixing) number of unknowns usually varies between N = 2 and 5 and the ...
2
votes
5answers
72 views

Why a linear numerator for fractions with irreducible denominators?

For example: (2x^3+5x+1)/((x^2+4)(x^2+x+2)) breaks down to (ax+b/(x^2+4))+(cx+d/(x^2+x+2)). I have been told that since the denominators are irreducible, the numerators will be either linear or ...
1
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3answers
66 views

Partial fraction decomposition of a complicated rational function

Find the partial fraction decomposition of the rational function $\displaystyle \frac{2x^3+7x+5}{(x^2+x+2)(x^2+1)}$ I have tried dividing first but keep running into problem after problem, please ...
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0answers
29 views

determine in what grid rhombus is a point

i have a rhombus ( i.e. diamond) grid determined by these equations ...
1
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1answer
53 views

Solve the system of equations…!

Can you please help me solve this system of equations (frankly I have no idea, it's the first equation of this type that I solve, so please, write only a hint): $$ \left\{ \begin{array}{c} x-\arctan ...
2
votes
3answers
28 views

Solve the following system of linear equations for any values of real parameter $a$…

For any values of parameter $a$ solve the following system of linear equations: $$\begin{cases} x+y+2z=1 \\ 2x+ay-z=4 \\ 3x+y+3z=1 \end{cases} $$ Calculating the value of determinant I found out, ...
0
votes
1answer
73 views

Linear systems. Please help me solve this

Please help me solve this. Consider for every real number $a$ the linear system of equations: $$ \begin{align} x +( a + 1 )y + a^2 z &= a^3 \\ (1-a)x +( 1 - 2a )y &= a^3 \\ x +( a ...
0
votes
1answer
38 views

Understanding a solution of a system of differential equations

I am looking at the system $$ x' = -y + xy^2 \\ y' = 4x - 4x^2 y $$ and trying to find its solution curves. I have a proposed solution to this which uses the fact that $$ \frac{dy}{dx} = ...
0
votes
1answer
21 views

Finding solutions using graph

Find the number of solutions of the equation $$|\ln|x|\;|=\sin(\pi x)$$ I know how to draw roughly the graph of $|\ln|x|\;|$. However, at $x=1$, both the graphs will pass through $(1,0)$. How do I ...
1
vote
1answer
58 views

Drawing the trajectories for a non-linear system

Find the critical points of the system and draw the trajectories, indicate if they are stable, asy. stable or unstable. $dx/dt=x(1.5-x-0.5y)\\dy/dt=y(2-y-0.75x)$ My critical points are $(0,0) ...