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.

learn more… | top users | synonyms (1)

0
votes
0answers
13 views

Singular solutions of a system of nonlinear 2nd order ODEs

I'm faced with the following nonlinear 2nd order system of ODEs: $$ \phi''(r)+\frac{4r^3-1}{r^4-r}\phi'(r)+\frac{r^2 h(r)^2+2r(r^3-1)}{(r^3-1)^2}\phi(r)=0, \\ ...
1
vote
0answers
8 views

Are there multiple solutions to this system of (two) equations? How can I know?

I have two equations: $$N_sc_s + p_s L =N_s \gamma^sw$$ and $$\frac{(1+g)N_s c_s}{\gamma} + \frac{(1+h)p_s L}{(1+n)\gamma} = N_s \gamma^s w$$ Where the variables are $c_s, p_s$. Obviously One way for ...
0
votes
0answers
15 views

satellites attitude determination TRIAD - how are orbital reference frame vectors constructed?

I posted this same question on space.stackexchange but never received any answer. So I am posting here hoping to get an answer as this is a quite mathematical topic. I am trying to fully understand ...
0
votes
1answer
15 views

Addition vs. Substitution method for Linear Systems of Equations with Parameters

I thought that solving a 2x2 linear system of equations using either the substitution method or the addition method (adding the two equations to eliminate a variable, then using the substitution ...
0
votes
0answers
15 views

Sufficient condition for simultaneous equations

So basically I solved a system of 6 simultaneous equations to get the conditions 1. $y_1 =y_2$ or $y_3=y_4$, 2. $y_1 =y_3$ or $y_2=y_4$, 3. $y_1 =y_4$ or $y_2=y_3$. which is necessary for 1. $x_1 ...
0
votes
2answers
30 views

How to solve $8x^3-6x+6xy^2=0=4y^3-4y+6xy^2$

How can I solve this system? $$ \left\{\begin{matrix} 8x^3-6x+6xy^2=0\\ 4y^3-4y+6xy^2=0 \end{matrix}\right. $$ I do $$ \left\{\begin{matrix} 8x^3-6x+6xy^2=0\\ 4y^3-4y+6xy^2=0 \end{matrix}\right. ...
2
votes
0answers
34 views

Find elevator height given rope length?

This question is deceptively difficult. I feel like it's probably some classic example somewhere, but I'm not sure how to describe it in enough detail to get valid results in searching online. ...
0
votes
2answers
34 views

$17x+11y \equiv 7 \pmod {29}$ and $13x+10y \equiv 8 \pmod {29}$. What are x and y?

Congruency question: if $17x+11y \equiv 7 \pmod {29}$ and $13x+10y \equiv 8 \pmod {29}$, we need to find $x$ and $y$. There may be more than one answer. Not sure how to go about this; any help ...
-1
votes
1answer
26 views

Inequalities (System) (solving it)

Solve the system of inequalities and indicate all the integers which are in the solution set: \begin{align*} 3−2a&<13 \\ 5a&<17 \end{align*} I solved it then i realized it said ...
1
vote
3answers
56 views

Solve nonlinear system of equations

Solve the system of equations $$\begin{cases}163-400z\sin{x}&=0\\-135z+85\cos{x}+61&=0\end{cases}$$ What is the best way of going about this? I rearranged the second equation for $z$ and ...
0
votes
0answers
13 views

Disadvantages of Taylor series method

There is method called Taylor series method to solve non linear equations iteratively. I am interested to know ,what are the disadvantages of using this method to solve. General Idea any one please?
0
votes
2answers
23 views

Evaluating condition for no roots using gauss jordan elimination

Find the number of values of $k$ for which the system of equations has no solution: $$(k+1)x+8y=4k$$ $$kx+(k+3)y=3k-1$$ This is the augmented matrix: $$\begin{bmatrix} k+1 & 8 & 4k ...
1
vote
0answers
36 views

Simultaneous equation with 6 equations, 6 unknows and a degre of 5

How do I solve this simultaneous $$a + b + c = 2\to (1)$$ $$ax + by + cz = 0\to (2)$$ $$ax^2 + by^2 + cz^2 = \frac{2}{3}\to (3)$$ $$ax^3 + by^3 + cz^3 = 0\to (4)$$ $$ax^4 + by^4 + cz^4 = ...
0
votes
1answer
27 views

General solution of a system of equations given a set of specific solutions

I'm pretty sure I did this right but I'd just like to check to make sure - I've been presented with the following problem: Given a non-homogenous system of equations with 4 variables so that the ...
1
vote
0answers
25 views

On a max-min problem from an exam.

I have asked a different question on the same exercise (from an exam) a couple weeks ago, I hope it is acceptable to have a different question on the same exercise, I searched the Meta and it seems ...
0
votes
2answers
41 views

When solving linear equations what does ${0x_n = 0}$ mean? What if the system is used to find Nash equilibrium?

When solving systems of linear equations one sometimes gets result like ${0x_n = 0}$ what does it mean for solving the system? Is it error on part of the solver or just feature of the assignment? ...
0
votes
1answer
38 views

show the Wronskian is constant

Let $p,q : \Bbb{R} \to \Bbb{R^n}$ and $H:\Bbb{R^n}\times \Bbb{R^n} \to \Bbb{R} $ and the hamiltonian system: $$ \begin{cases} \dot p = - \frac{\partial H}{\partial q} \\ \dot q = \frac{\partial ...
8
votes
1answer
103 views

Solve: $x = (x-\frac{1}{x}) ^ {1/9} + (1-\frac{1}{x})^{1/9}$

Solve: $$x = \left(x-\frac{1}{x}\right) ^ {1/9} + \left(1-\frac{1}{x}\right)^{1/9}$$ Simplifying, $$x^{10/9} = (x^2-1)^{1/9}+(x-1)^{1/9}$$ I don't know how to start. Any hint will be helpful.
0
votes
0answers
14 views

range of $\phi$ in given trigonometric equation

Let $\theta,\phi\in[0,2π]$ be such that $2\cos(\theta)(1-\sin(\phi)=\sin^2\theta(tan(\theta/2)+\cot(\theta/2))\cos\phi-1,\tan(2π-\theta)>0,-1<\sin(\theta)<\sqrt{3}/2$ then $\phi$ cannot ...
0
votes
1answer
34 views

Simultaneous equation with summation and square - how to solve?

$\mathbf{p}$ is a vector with dimension: $x \times 1$ $\mathbf{d}$ is a vector with dimension: $1 \times y$ $\mathbf{V}$ is a matrix with dimension: $x \times y$ $y \geq x$ $\mathbf{d}$ and ...
0
votes
0answers
19 views

Prove that the solutions of ODE system are globally defined

Consider the folloing ODE system: $$x'(t)= A(t) x(t)+ b(t)$$ $$x(t_0)=x_0$$ Show that the solutions of the system are globally defined. Hint: We have to use gronwall inequality lemma. Could ...
-1
votes
2answers
61 views

Solve a system of two equations with cubic radicals

Solve the following system of equations ($x,y \in \Bbb R$): $$\begin{cases} (8x-13)y&=(x+1)\sqrt[3]{3y-2}-7x \\ (y-1)x^2+(8y+7)x&=y^2+12y+(x+1)\sqrt[3]{3y-2}. \end{cases}$$ I think this ...
3
votes
2answers
35 views

Calculations with an exponentially-weighted moving average

I need help figuring out the following formula: Where: CTLy = yesterdays CTL TSS = current Training Stress Score TC_c = your CTL Time Constant Now I have TSS, thats a number between 20-500 ...
-1
votes
0answers
64 views

Show that there is a limit cycle in the dynamical system

I have the dynamical system \begin{align} \dot{x}_1 & = -x_2+x_1(1-x_1^2-x_2^2), \\ \dot{x}_2 & = x_1 + x_2(1-x_1^2-x_2^2) \end{align} With the initial conditions $x_1(0)=x_{10}$ and ...
1
vote
3answers
49 views

what is the fastest way to solve equations having more than two variables of 1 degree?

Suppose I have four equations for four variables $$a+b+c+d=0$$ $$5a+3b+2c+6d=10$$ $$12a+21b+c+4d=30$$ $$2a+3b+4c+5d=40$$ Now what is the fastest way to find a, b, c and d? I know of elimination and ...
0
votes
1answer
27 views

overflow, round-off error

a) If the following function is written in a program, in what range of x would overflow or zero divide originated from round-off error occur? $f(x) = \frac{1}{1-tanh(x)}$ Assume that the ...
0
votes
1answer
23 views

Linear Algebra Systems of Equations

I'm just starting out, so please bear with me. While solving systems of equations in linear algebra, can you straight-up add, if two factors cancel? My problem: $$x_1 + 3x_2 -x_3 +x_4 +2x_5 = ...
4
votes
2answers
246 views

Is there any easy way to solve two equations with three unknowns?

Is there a way to solve the below simultaneous equations? One possible solution is $a_1=20.0948$, $a_2=10.0948$, $a_3=6.3448$. The variables are actually dual variables of the binding constraints. ...
2
votes
2answers
41 views

Solving for the positions of vertices of 3 line segments

I have 3 line segments of lengths p,q,r joined at their ends. Let's call the vertices A, B, C, and D. Suppose D is fixed at the origin. Suppose that A is constrained to move only in the Y direction. ...
1
vote
2answers
32 views

Find all $n$ such that $m = an$ or $m =\dfrac{n}{a}$

$a$ is the 1st digit (from the left) of a $3$-digit number $n$. We get the number $m$ by removing a from $n$ and putting it on the right of the unit-digit. For example, the number $123$ becomes $231$. ...
0
votes
0answers
23 views

Companion matrix of bivariate polynomial

A polynomial in one variable can be expressed as a companion matrix, of which the eigenvalues are the roots of the polynomial and which can be found by using e.g. QR decomposition or power iteration. ...
1
vote
1answer
26 views

Triple Simultaneous Equations not resolving the Equation for a Quadratic Function

so I'm doing this math problem for my Calculus I course in college. Here is a screenshot of the problem: Graph 1 (click here to view); the prompt is "Find an expression for the quadratic function ...
0
votes
1answer
38 views

Linear systems of equations and vector spaces

I'm looking for references that explicitly (and in an accesible way: -I come from engineering-) handle the connection between solving a linear system of equations and the abstract geometry involved.
0
votes
0answers
19 views

How to rewrite a system of two non-linear equations in order to make evident a property of the solution

I know this is non-general and may look uninteresting but asking is worth a try. I have the following system of two non-linear equations (in two unknowns x and y and two parameters a and p) that I ...
0
votes
1answer
21 views

Why Non Linear equations put equal to zero in Newton Raphson Mehotd

While solving non linear equations we put them equal to zero in Newton-Raphson Method.Why we do that? Any Idea?
1
vote
1answer
52 views

Launching a Plaintext Attack against Affine Cipher

Update 2 Being new to the world of Stack Exchange I did not realize that there exists a site solely devoted to cryptography. In light of this, I hope someone could help me migrate this question to ...
0
votes
1answer
26 views

Profit and loss question.

A person bought two bicycles for Rs.1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the seconds at 10% profit .He would get Rs.5 more.The ...
1
vote
0answers
23 views

Show that the determinant is the Wronskian

Prove that the determinant of the following system $(\star)$ is the Wronskian. $$(\star) \begin{pmatrix} y_1(s) & -y_2(s)\\ -y_1'(s) & y_2'(s) \end{pmatrix} \begin{pmatrix} c_1(s)\\ c_2(s) ...
1
vote
1answer
20 views

On solving systems of nonlinear equations.

I was tasked with solving (obtain explicit solutions without utilizing complex coordinates) this system of non-linear equations as part of an exam, \begin{cases} 2z e^{xy} +2 \lambda z - 2 \lambda ...
0
votes
0answers
31 views

Comparison between Laplace, operator calculus and system of first order ODE

I am trying to understand those three methods to solve differential equations. I would like to know what actually are the differences between the three: Laplace calculus operator conversion to a ...
0
votes
1answer
32 views

Simple system of two nonhomogeneous ordinary differential equations solved by elimination. (3.1-25)

My differential equations textbook states to use the "elimination method" to crack this for $x$ and $y$. The final answer uses $t$ as the independent variable which both $x$ and $y$ are dependent on. ...
0
votes
0answers
9 views

An algebraic equation system and the Jacobi determinant as test for its solvability

I am trying to verify a result in a text that I am currently reading. The context is in algebra and combinatorics. However the result is obtained by using a bit of vector calculus much to my suprise. ...
0
votes
1answer
120 views

Exact solution to system of first order ODEs

I am trying to solve a system of 1st order ODE's. $m(r)$ and $P(r)$ are real functions of $r$ and should be positive. $a$ and $b$ are just constants. $$\frac{d m(r)}{dr}=\pi(\frac{P(r)}{a}+b)r^2\\$$ ...
2
votes
3answers
76 views

How can you find $m$ in $mx^2+(m-3)x+1=0 $ so that there is only one solution

How can you find $m$ in $$mx^2+(m-3)x+1=0 $$ so that there is only one solution. I tried to solve it by quadratic equation but I end up with two solutions. So I want it know that is there a way so ...
0
votes
1answer
93 views

Can this nonlinear simultaneous equations be solved?

Problem: Can this nonlinear simultaneous equations be solved about $\mathbf{x}$? Then $\{A,B,E\}\in R^{n \times n}$ are symmetric matrices, $\{\mathbf{x},\mathbf{y}\}\in R^{n}$. Particularly, $E$ is ...
1
vote
1answer
40 views

solve in positive integers $x$ and $y$

Solve the equation for positive integers $x,y$ $$y^3+3y^2+3y=x^3+5x^2-19x+20$$ i have written the equation as $$(y+1)^3=x^3+5x^2-19x+21$$ which is $$(y+1)^3-x^3=5x^2-19x+21$$ and by using ...
-1
votes
1answer
35 views

Solve the following equation: [closed]

\begin{align*} 7yz+3zx&=4xy,\\ 21yz-3zx&=4xy,\\ x+2y+3z&=19. \end{align*} Answer: $(x,y,z)=(7,3,2)$ I'm not able to solve this. Steps?
1
vote
1answer
43 views

Algebraic elimination: Subtracting one equation from another

I'm studying basic polynomial math online and I ran into this situation: $$2a + b = 8 \\ a + b = 5$$ The course material infers, using this exact notation, that: $$2a + b = 8 - (a + b = 5) = a = ...
1
vote
1answer
40 views

Proof of $xy\ge4$ with $x=z+\frac{1}{p}$ and $y=p+\frac{1}{z}$, where $x,y,z,p \in R$ $x,y,z,p\gt0$

Consider following set of equations: $$x=z+\frac{1}{p}$$ $$y=p+\frac{1}{z}$$ Where $$x,y,z,p \in R$$$$x,y,z,p\gt0$$ How to prove: $$xy\ge4$$
0
votes
1answer
23 views

Find element of a one vector to form a basis with existing vectors

Let $a=(1,2,-1),b=(1,1,1),c=(1,3,\lambda)$ are given vectors. Find $\lambda$ such that the given vectors form a basis for in $\mathbb{R^3}$. For each found $\lambda$ represent a vector $v=(1,1,2)$ in ...