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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15 views

Variable bounds of under-determined linear system

If I have a non-negative, under-determined linear system $\mathbf{Ax}=\mathbf{b}$ $\mathbf{x}\geq\mathbf{0}$ is there a fast way to compute the upper and lower bounds on values of each element of ...
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0answers
49 views

Predator Prey Equation

The Predator-Prey Equation is outlined by the following equation: $$\left\{ \begin{array}{l} \frac{dx}{dt}=\alpha x-\beta xy \\ \frac{dy}{dt}=-\gamma y+\delta xy \end{array} \right.$$ Can someone ...
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4answers
64 views

solving the system

solve the system : $$ y+|x-2|=3 $$, $$ |x+y|= m $$ graphicly when $m$ equals $6$. I can easily (realtively) skecth the first graph , however, how the bloody hell do you sketch $|x+y|= 6$??
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3answers
421 views

How to solve a system of three nonlinear equation in a simple way

Given the system: $$ \begin{cases} x^2y^2+x^2z^2=axyz & \\ y^2z^2+y^2x^2=bxyz &\\ z^2x^2+z^2y^2=cxyz \end{cases} $$ The solution could be gotten in a very tedious way. Is ...
3
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1answer
88 views

how to solve these equation?

For $a , b , x , y$ are members of $\mathbb{R}$ If $ax+by=3\\ax^2+by^2=7\\ax^3+by^3=16\\ax^4+by^4=42$ then $ax^5+by^5=?$ a lot of thanks for all comments
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0answers
22 views

Removing parametrization from a system of equations

Consider the following system : $$ \begin{aligned} \frac{d^2t}{d\lambda^2} &= -f\left(t\right)\frac{d t}{d \lambda}\frac{d t}{d \lambda} -A\frac{d g\left(t,x\right)}{d \lambda}\frac{d t}{d ...
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2answers
78 views

System of non-linear ODE's

do you have any suggestions to solve analytically the Non-linear ODE system $\dot x=18 x^2 y-3p x^2+6p xy$ $\dot y=18 x^2 y-6p xy $ where $p$ is a real constant. Thank you very much cheers
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0answers
18 views

System of ODE's with varying times.

Sorry for the vague question, I wasn't really sure how to phrase this. This isn't for homework, it's a problem I am working on. It's been a long time since I've taken differential equations and I'm ...
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4answers
760 views

How find the value of the $x+y$

Question: let $x,y\in \Bbb R $, and such $$\begin{cases} 3x^3+4y^3=7\\ 4x^4+3y^4=16 \end{cases}$$ Find the $x+y$ This problem is from china some BBS My idea: since ...
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3answers
28 views

Iterative Equation Problem with Constraints

I was given a programming riddle recently. It was eluded to that there is an equation, but I was told that finding the equation was not the goal, and that writing a simple program was the goal. I ...
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4answers
85 views

Solve the System of Equations in Real $x$,$y$ and $z$

Solve for $x$,$y$ and $z$ $\in $ $\mathbb{R}$ if $$\begin{align} x^2+x-1=y \\ y^2+y-1=z\\ z^2+z-1=x \end{align}$$ My Try: if $x=y=z$ then the two triplets $(1,1,1)$ and ...
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0answers
47 views

Underdetermined system of equations

I am sorry in advance if the question I am going to ask is trivial. I have a problem of underdetermined system of equations (6 unknowns and three equations).All unknowns are between 0 and 1. Are there ...
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1answer
19 views

system of equations with coefficients in finite field

Suppose we have three simultaneously equations with $4$ variables with coefficients in finite fields, i.e. $$\alpha_1A_1 + \beta_1B_1+\gamma_1C_1 + \theta_1D_1=x$$ $$\alpha_2A_1 + ...
3
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1answer
27 views

Find the polynomial function

Anybody knows how to find the polynomial function with evaluated values, where if the degree is $n$ I have $n+1$ values of the function like $f(0) = a_0, f(1) = a_1, \ldots, f(n) = a_n$.
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0answers
17 views

bounds of solution to the system of nonlinear equations

I have a system of nonlinear equations: \begin{eqnarray*} F_1(x,y) &=& 0,\\ F_2(x,y) &=& 0, \end{eqnarray*} where $F_i(x,y)$ with $i=1,2$ are continuosly differentiable in $(x,y)$. ...
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3answers
33 views

Prove that $b^2 pr =q^2 ac$ using matrices

Let $i_1,i_2$ and $j_1,j_2$ be non-zero real roots of $ax^2+bx+c$ and $px^2+qx+r$ respectively, where a,p $\neq$0. If the system of equations $ i_1y+i_2z=0$ and $j_1y+j_2z=0$ has a non-trivial ...
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1answer
61 views

Solving system of two linear odes

I am trying to solve \begin{align} y_1'+B_{12}y_1=\beta_{12}y_2\\ Ay_2'+B_{21}y_2=\beta_{21}y_1, \end{align}with $y_1(0)=y_2(0)=y_0$. I find the eigenvalues to be ...
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0answers
24 views

Solution of a DAE system of two ODE of second degree

I should solve the following DAE system: $$\ddot{x}(t)=-\alpha y(t)$$ $$\ddot{y}(t)=\beta x(t)$$ with the conditions: $x(t)\ge0$, $y(t)\ge0$ and $x(t)+y(t)=N$ with $N\gt 0$. I'm able to solve the ...
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1answer
40 views

Solving an augmented coefficient matrix so there are infinitely solutions

I am trying to figure out this math problem. For what values $a,b$ does the linear system have infinitely many solutions? This is the matrix $$ \left[ \begin{array}{ccc|c} ...
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2answers
57 views

For which values of $a, b$ does the system of equations NOT have any solutions?

I am trying to solve this math problem: For which values of $a$ and $b$ does the linear system represented by the augmented matrix not have any solution? $$ \left[ \begin{array}{ccc|c} ...
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1answer
38 views

Solve a system of equations.

I have a system of equations: \begin{align} & x_{21} (\frac{\partial}{\partial x_{11}}f_{1111})( x_{11} , x_{21}, y_{11} , y_{21} ) + \frac{y_{21}}{x_{11}^2} (\frac{\partial}{\partial ...
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1answer
33 views

Cramer's rule and linear dependence/independence test

When you have the system of equations: $$ax + by = e\\cx + dy = f$$ And you do some row operations to eliminate $y$, we get: $$x = \frac{ed-bf}{ad-bc}\tag{1}$$ If we eliminate $x$ we get: $$y = ...
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0answers
32 views

Converting sums to matrix equations

I am able to transform basic sums to vector/matrix equations. But now I have something like: $$ c_{p,q} = \sum_{n=1}^N \sum_{r=1}^R \sum_{s=1}^S e_n x_{n-q-s,p} \cdot h_{r,s} \cdot g_r \cdot ...
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1answer
22 views

Help inverting a non-linear system of equations

I have a set of two equations like this $$ \gamma_3=\left(\frac{1}{\sqrt{1+2c_3^2+6c_4^2}}\right)^3 \left( \alpha_1\,c_3^3 + \alpha_2\,c_3c_4^2 + \alpha_3\,c_3c_4 + \alpha_4\,c_4\right)\\ ...
1
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1answer
54 views

How can I write a system of equations puzzle if given the solutions? (work backwards?)

\begin{matrix} a = 12 & b = 6 & c = 5 & d = 1 & e = 0\\ \end{matrix} How can I create a fun puzzle or word problem that would arrive at this solution above? For example, ...
4
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3answers
83 views

Pair of PDEs to be solved together

I have the following pair of equations to be solved together to find the functions $H_{x}$ and $H_{y}$, which are the components of a vector $\bar{H}(x,y)=H_{x}(x,y)\hat{x}+H_{y}(x,y)\hat{y}$ in ...
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2answers
54 views

Solving coupled first-order linear ODEs

Basically this question comes from population modelling. Let y be the population of Lions and let x be the population of deer. By ignoring the effect of deer, we observe that $$dy/dt = k_2 y$$ ...
1
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1answer
34 views

Find the equation of the plane passing through $P(0,0,1)$ and containing $x=y=z$

Find the equation of the plane passing through $P(0,0,1)$ and containing $x=y=z$ a) y-z=0 b) x-z=0 c) z+x=1 d) x-y=0 My attempt: I considered the point $P(0,0,1)$ for hypothesis and ...
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0answers
47 views

Time needed to algebraically solve system of $15$ nonlinear equations with parameters

How long can I expect it will take to algebraically solve a system of $15$ nonlinear equations (without any numbers, only parameters), if I feed it into a computing software? I'm asking for symbolic ...
2
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2answers
74 views

How prove this equation have more one solution $x_{1}+x_{2}+\cdots+x_{n}=d,x_{1}x_{2}\cdots x_{n}=b$

Let $x_{i}\in \mathbb{Z},i=1,2,\ldots,n$, and such that $1\le x_{1}\le x_{2}\le\cdots\le x_{n}$. Show that $$\begin{cases} x_{1}+x_{2}+\cdots+x_{n}=d\\ x_{1}x_{2}\cdots x_{n}=b\\ b,d\in \mathbb{Z} ...
11
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1answer
152 views

Cyclic system of equations

Consider the system of equations $$ \begin{align*} x^2+(1-y)^2&=a\\ y^2+(1-z)^2&=b\\ z^2+(1-x)^2&=c\\ \end{align*} $$ Compute $x(1-x)$ in terms of $a,b,c$. Edit: The question should say ...
2
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2answers
69 views

How to determine the eigenvectors for this matrix

I have the matrix $$\left( \begin{array}{ccc} -\alpha & \beta \\ \beta/K & -\alpha/K \end{array} \right)$$ for which the eigenvalues are ...
2
votes
1answer
71 views

a system of finite difference equations

Let $a,b>0$ such that $ab<1$ consider the system$$x_{t+1}=x_ty_t+ay_t$$ $$y_{t+1}=x_ty_t+bx_t$$ I would like you to help me answer the following: find values $a$ and $b$ ​​for which the ...
0
votes
1answer
32 views

Gaussian elimination easily?

Let $$\left( {\matrix{ 1 & 0 & { - 3} \cr 0 & 2 & {\lambda + 3} \cr 0 & 0 & {5 - {\lambda ^2}/2 - 3\lambda /2} \cr } \left| {\matrix{ { - 3} \cr 2 ...
1
vote
1answer
59 views

Solving non-linear (convex) systems of equations

I have a system of non-linear equations that takes the following form \begin{align} \left[ \begin{array}{c} y_1 \\ y_2 \\ \vdots\\ y_n \end{array} \right] = \left[ \begin{array}{c} f_1({\bf ...
0
votes
3answers
38 views

Find the solutions set for a linear system

Let $$\left\{ {\matrix{ {a_1x + b_1y + c_1z = d_1} \cr {a_2x + b_2y + c_2z = d_2} \cr {a_3x + b_3y + c_3z = d_3} \cr } } \right.$$ It's given that the unique solution for the system ...
1
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4answers
77 views

The relation between $\det(A)$ and $Ax=b$

I wish to understand the the relation between $\det(A)$ and $Ax=b$. Hence, what are the solutions for $Ax=b$ (homogeneous and non-homogeneous) when $\det(A)=0$ and $\det(A)\ne 0$? So, all in all ...
2
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1answer
106 views

Three phase voltage system of polynomial equations

I'm working with the development of a product in the company where I work. This product measures three phase voltages and currents. I cannot change the circuit because it has been sold for a long time ...
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1answer
28 views

How do I modify a system of equations to receive unlimited solutions (SAT Question)

I am sorry that I don't have a specific question (it was on my sat make-up) but I remember a question that went something like 3x + 2y = 26 and another part of the system of equations that I don't ...
0
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1answer
51 views

How to solve these two differential equation?

I try to solve these two difference equation ; $$ \frac{dq}{dz} = -j\left(b_1q - kp\right),\\ \frac{dp}{dz} = -j\left(b_2p - kq\right) $$ where $j$ stands for $\sqrt{-1}$, and $b_1$ ,$b_2$ and k are ...
0
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0answers
34 views

Nondimensionalization of Coupled ODE

So what I'm messing around with are these two coupled ODES: $$\frac{dx}{dt}=\gamma x\left(1 - \frac{\alpha x+\beta y}{N}\right)$$ $$\frac{dy}{dt}=\theta y\left(1 - \frac{\alpha x+\beta ...
5
votes
1answer
104 views

When is the equation $Ax = b$ solvable in the integers?

Let $A$ be an $m\times n$ matrix with integer entries, $b$ a column-vector with $m$ integer entries. Suppose the equation $Ax = b$ has infinitely many solutions. It is clear that the general ...
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0answers
20 views

system of two quadratic equations with two variables

Is there a general way to solve exactly a system of this shape (the $a_i$ are constants): $$\begin{array}{cc}a_1x^2+a_2x+a_3y^2+a_4y+a_5=0\\ a_6xy+a_7x+a_8y+a_9=0 \end{array} $$ It comes from a ...
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1answer
23 views

Solving $x' = Ax$ for real $x$ where $A$ is a matrix with complex eigen values

I have the following linear differential equation system: $$x' = A x$$ where $$ A = \left( \begin{array}{ccc} 1 & 0 & 0 \\ 3 & 1 & -2 \\ 2 & 2 & 1 \end{array} \right) $$ I ...
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0answers
22 views

System of ODEs and DAE system

Let us consider the following system of ODEs: $$ y' = f(y,z),\quad z' = g(y,z),\quad y(0) = y_0,\;z(0)=z_0 $$ and the following one: $$ y' = f(y,z),\quad 0 = g(y,z), \quad y(0) = y_0. $$ $f$ and $g$ ...
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2answers
60 views

Find conditions on a, b, c, and d for which the following system has solutions:

Find conditions on $a$, $b$, $c$, and $d$ for which the following system has solutions: $$2x+4y+z+3w=a $$ $$-3x+y+2z-2w=b $$ $$12x+5y-4z+12w=c $$ $$13x+10y-z+13w=d$$ I got the system down to: ...
0
votes
1answer
28 views

Solutions of a system of linear equations with a parameter

I've come across a linear algebra problem that I'm not sure how to solve. It's a generic problem - I have to find the solutions of a system of equations dependent on a parameter. So, my first though ...
0
votes
0answers
56 views

Blowing-up a singular point

I have this system of ODEs: $$x'=-y+ \mu x(x^2+y^2)$$ $$y'=x+ \mu y(x^2+y^2)$$ I already find that in $\mathbb{R}^2$ the only singular point is $(0,0)$. So I have to blow-up the singularity to find ...
0
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1answer
36 views

Fastest way to compute minimal polynomial (for solving $x' = A x$, $A$ matrix)

In general, given a $3\times 3$ or $4\times 4$ matrix $A$ which doesn't have a lot of $0$ entries, what is the fastest or less error prone way to compute its minimal polynomial? More generally, I ...
0
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2answers
36 views

Solving $\left\{\begin{matrix}u'v''-u''v'=0 \\ R^2u'u''+v'v''=0 \end{matrix}\right.$.

Given that $u,v$ are functions of $t$, $R$ constant, solve $\left\{\begin{matrix}u'v''-u''v'=0 \\ R^2u'u''+v'v''=0 \end{matrix}\right.$. When trying to find geodesic on cylinder, I get this ...