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
14 views

number of solutions of system of two equations, two unknowns (Matrix)

How can we find that when a system of two equations, two unknowns has Infinite Solutions. I want a solution with matrix. I know this method (which is not with matrix): $ax + by = c$ $a'x+ b'y = c'$ ...
0
votes
0answers
14 views

Issue on solving System of Equation regarding Nested Radicals

I was reading on about nested radicals on an earlier asked question, and I didn't quite understand what he meant about "substituting these into (3),(4), we get b,c for arbitrary a". If he's saying ...
0
votes
0answers
38 views

Solution to System of Complicated Differential Equations

I'm looking for a solution to this set of complicated differential equations: $$\begin{align} \dfrac{dθ}{ds} & = \dfrac{\cos θ}{r} − z\\ \dfrac{dz}{ds}& = − \cos θ \\ \dfrac{dr}{ds} &= ...
1
vote
1answer
16 views

How to determine if an object in space is pointing at (oriented toward) another object?

QUESTION: You know the position of two objects in space (one also has an orientation). How do you determine when the object is pointing/oriented at the other object? Hopefully this question makes ...
-2
votes
2answers
58 views

Simple but hard 2 by 2 system in $x$ and $y$ [duplicate]

Is there a systematic way of solving this system, analytically? $$\begin{cases} x \ + \ y^2=11\\ x^2+y\ \ =\ 7\\ \end{cases} $$ I mean, other than brute-force.
0
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0answers
28 views

Probabalistic solve of system of equations

I'm engineer, not mathematician, so excuse me for wrong terminology, but I hope you'll understand the problem. Example situation: I have N electronic components. Each of them has reactance and ...
3
votes
3answers
31 views

Maximize system of linear equations

Suppose you have the system $$ \begin{bmatrix} 4 & 3\\ 1 & 7\\ 5 & 9\\ 2 & 4\\ \end{bmatrix} \begin{bmatrix} x\\y\end{bmatrix}=\begin{bmatrix}b_1\\b_2\\b_3\\b_4\end{bmatrix} $$ How ...
0
votes
0answers
16 views

Solve the EDO $p'={\alpha}p^a+{\beta}p^b,\quad t>0,$

Fix $\alpha , \beta \in (0,\infty)$ . Use Osgood's criterion to show that the equation $$p'={\alpha}p^a+{\beta}p^b,\quad t>0,$$ has at most one nonnegative solution if $a,b \ge 1$. Also, prove ...
0
votes
1answer
16 views

Value of $a$ if system of equation is consistent.

If the following equations are consistent and have more than one solution, what is the value of $a$? Given $u+v=-(av+1)$ $u+2v=-a(v-1)$ $3u+8v=a+2$ I was thinking that system of equation is ...
0
votes
0answers
40 views

Linear system equations

I need to get, preferably by a numerical method, a solutions of: $$\left\{\begin{array}{lll} 2\sum_{i=1}^n b_{ik}x_i+x_{n+1}=0&\text{for}& k=1,2\ldots,n\\ \sum_{i=1}^n x_i=0 ...
0
votes
0answers
31 views

Solving system of nonlinear equations via iteration

I will give an example to illustrate the question: Assume I have the system: $$ xy + x + y = 7\\ x^2 + y^3 = 9 $$ and I want to solve for $x$ and $y$. It is a fairly common approach to rearrange ...
1
vote
2answers
30 views

Decouple a system of two second order differential equations

I have a system of second-order differential equations that I want to decouple. they are, $\ddot{x} = \frac{\omega_1^2}{2} x + \omega_2 \dot{y}$ and $\ddot{y} = \frac{\omega_1^2}{2} y - \omega_2 ...
-4
votes
0answers
26 views

How do I solve these questions? [on hold]

A person receives Rs 6,000 per month salary.If his monthly salary is incremented by Rs 300 every year,what amount he would receive in 30 years? a 43,10,000 b 37,26,000 c 23,10,000 d 52,92,000 Q2 ...
1
vote
3answers
23 views

Process for solving this system of equations

I have this system of equations for which I'd like to solve for $x$,$y$, and $r$ where $a$,$b$, and $t$ are constants: 1: $0 = (x-a)^2 + (y - b)^2 - t^2$ 2: $y = \dfrac{bx-rx+ar}{a}$ 3: $r = ...
0
votes
1answer
36 views

How to solve simultaneous inequalities (reasked)? [duplicate]

I am doing multivariable calculus, and specifically double integrals. I am facing difficulties finding the domain of the integal, however i am given the following equations: $$1≤2x+y≤2$$ $$0≤x−2y≤1$$ ...
-2
votes
1answer
23 views

Find an energy functional for the nonlinear viscous oscillator $x' = v$, $v' =-b(v)v-k(x)x$, $t>0$ [on hold]

Consider the nonlinear viscous oscillator $$\begin{cases} x' = v\\ v' =-b(v)v-k(x)x,\quad t>0, \\ \end{cases}$$ where $(x,v)$ is the position and velocity of the oscillator. Here $b : \mathbb ...
-1
votes
0answers
16 views

Use Osgood's criterion and comparison principle to show that the equation $p'={\alpha}p^a+{\beta}p^b$ has global and local solutions. [on hold]

Fix $\alpha , \beta \in (0,\infty)$ . Use Osgood's criterion to show that the equation $$p'={\alpha}p^a+{\beta}p^b,\quad t>0,$$ has at most one nonnegative solution if $a,b \ge 1$. Also, prove ...
0
votes
1answer
19 views

Showing that a system has a unique steady state at $(0, 0).$

Consider a system: $$ dx/dt = y + x(2 − x^2 − y^2 ), $$ $$dy/dt = −x + y(1 − x^2 − y^2)$$ (i) Show that the system has a unique steady state at $(0, 0).$ My immediate thought is to ...
0
votes
0answers
6 views

Hyperplane and cubic curves and their intersections.

Solve the following: $$a^4-a^2+A_{1}E u=0;$$ $$b^4-b^2+A_{2}Eu=0;$$ $$c^4-c^2+A_{3}Eu=0;$$ $$d^4-d^2+A_{4}Eu=0;$$ and $$a^2+b^2+c^2+d^2=E,$$ for $a, b, c, d,$ and $u$, when $A_{1}, A_{2}, A_{3}, ...
1
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0answers
24 views

Counting the isotropic points for both quadratic and hermitian forms.

Consider an octonion algebra $\mathbb{O} = \mathbb{O}_{\mathbb{F}_{q^2}}$ over a field of order $q^2$, $q = p^k$. Then we have a natural quadratic and hermitean (by this I actually mean hermitean ...
0
votes
1answer
28 views

Question regarding systems of equations

If I have the following system of equations: $2+x^2-y^2=0$ $x^2-y^2-2=0$ And if I substitute $y$ by a function of $x$ and vice versa I get: $2+x^2-x^2+2=0$ $y^2-y^2-4=0$ I therefore get: ...
0
votes
0answers
20 views

Linear algebra: Solving for the coefficients on vectors

I am solving the following system: $$ -\frac{1}{r^2}\begin{bmatrix}\sqrt{\mu}\cos(\theta)\\ \sin(\theta) \end{bmatrix}= ...
0
votes
2answers
43 views

Find the eigenvector and eigenvalues for the following 3 x 3 Matrix?

$$ \pmatrix{5 & 8 & 16 \\ 4 & 1 & 8 \\ -4 &-4 & -11} $$ I already got the eigenvalues that is $\lambda = 1$ and $-3$. And I managed to solve the eigenvector corresponding to ...
3
votes
5answers
64 views

Solution of $x^y=y^x$ and $x^2=y^3$

Solve the given set of equations: $x^y=y^x$ and $x^2=y^3$ where $x,y \in \mathbb{R}$ Would any other solution exist other that $x=y=1$ because I think $x^2=y^3$ will only be true for $x=y=1$ or ...
0
votes
1answer
21 views

Point of intersection of ellipses

If two ellipses are intersecting at a point,is it necessary that the line drawn joining the centre of those two ellipses should also pass through the point of intersection (of ellipse)? (if yes,how to ...
0
votes
0answers
18 views

Solving systems of linear equations with complex numbers by hand

How can I solve a 3x3 system of linear equations with complex numbers by hand without making a mistake? I know that I can solve them either with Gaussian Elimination or Cramer's rule, but I find it ...
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votes
0answers
18 views

Does a row echelon form have to follow the same order of zero placement? [on hold]

Can an echelon form involve zero's in different positions even if it fulfils the same requirements? Example matrix which solves like an echelon form but in different order Is this also considered ...
1
vote
1answer
48 views

How to estimate the parameters of a logistic differential equation from the values of its solution at times 0, 1 and 2?

How do I solve this system of equations? I received these equations after letting Wolfram Alpha solve the logistic differential equation $$N'(t)=kN(t)(M-N(t)),\qquad N(0)=65,$$ that outputs: ...
0
votes
1answer
40 views

Solve $Ax=b$ for $A$ in MATLAB

I have this linear system $$\begin{bmatrix} cY(t-1)\\ acY(t-1) - acY(t-2)\end{bmatrix} = T \begin{bmatrix} Y(t-2)\\ Y(t-1)\end{bmatrix}$$ where both $c$ and $a$ are known constants, and I need to ...
0
votes
2answers
80 views

Solve the simultaneous equations for real numbers $x$ and $y$: $ \sqrt{x+a} + \sqrt{x-a} = 3 $ and $ x+y=5 $

Question: Let $a$ be a real number. Solve the simultaneous equations for real numbers $x$ and $y$: $$ \sqrt{x+a} + \sqrt{x-a} = 3 $$ $$ x+y=5 $$ My attempt: Consider ...
2
votes
0answers
35 views

Solving a 1D integral with system of equations for retarded electromagnetic fields

I need to solve the following integral to calculate the effect of retarded electromagnetic fields on a test charge: ...
1
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2answers
43 views

Solving a system of equations which contain sin and cosine terms.

Hello my question is the following: Solve the given system of equations: $$E=\frac{l_{p}}{\pi}\sqrt{\sin^{2}\left(\frac{\pi y_{1}}{l_{p}}\right)+\sin^{2}\left(\frac{\pi ...
0
votes
1answer
72 views

When I know $a+b+c, a^2+a^2+b^2, a^3+b^3+c^3$, then how can I find the $a$ and $b$ and $ c$ [closed]

When I know $$a+b+c = A$$ $$a^2+a^2+b^2 = B $$ $$a^3+b^3+c^3 = C$$ Then how can I find the $a$ and $b$ and $c$?
0
votes
1answer
30 views

Solutions to set of equations involving prime numbers

Is there a collection of distinct positive integers $(k_1, k_2, k_3, p_1, p_2, p_3)$ such that: $p_1, p_2, p_3$ are odd primes, and $k_1, k_2, k_3$ are odd $(k_1 + 2) p_1 = k_2 p_2$ and $(k_2 + 2) ...
1
vote
0answers
23 views

Transform the system of trigonometric equations

How to extract $\ell$ and $L$ from the following system of equations: $$\alpha=\arctan {R_E \cos \ell \sin L \over R_0 + R_E(1 - \cos \ell \cos L) }$$ $$\beta=\arctan {R_E \sin \ell \cos \alpha \over ...
4
votes
2answers
83 views

How to solve simultaneous inequalities?

I am doing multivariable calculus, and specifically double integrals. I am facing difficulties finding the domain of the integal, however i am given the following equations: $$1 ≤ 2x+y ≤ 2$$ $$0 ≤ ...
1
vote
1answer
45 views

solve pairs of two variable simultaneous linear modular equations

I’m looking for a method to solve pairs of simultaneous linear modular equations, such as 323x + 37y = 0 Mod 243; -397x + 683y = 0 Mod 32 I’ve simplified this to 80x+37y = 243g; 19x+11y = ...
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0answers
33 views

Does anyone have nice explanation about the theory? [closed]

I have hard time interpreting the Floquet theory. Does anyone have nice explanation about the theory?
0
votes
1answer
14 views

Arbitrary variable in matrix, when there are 0 solutions, 1 solution, infinitely many solutions

For what value of the constants k does the system have (i) no solutions, (ii) infinitely many solutions, (iii) a unique solution? $$ x − 2y + z = 7\\ x − 2y − kz = k\\ kx − 2y + kz = 7 $$ At ...
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votes
2answers
31 views

Figuring $x$ and $y$ from two linear equations

I have a mini exam in a month to study for and I'm looking at systems of equations at the moment. I have this question to look at right now: Find $x$ and $y:$ $x-5y+4=1$ $\dfrac{x+1}{2}=y^2$ Now ...
4
votes
0answers
100 views

Large system of nonlinear equations

I am trying to solve a problem, which I find quite hard, like, headache-hard. I have to solve the following set of $M$ nonlinear equations: $$F(X)=\begin{bmatrix}f_1 (X)\\f_2 (X)\\...\\f_M (X)\\ ...
3
votes
1answer
41 views

Solution to a simple system of quadratic equations

I am hoping to find a closed-form solution to the following system of $n$ quadratic equations: $$ x_j^2 = \sum_{i=1}^n B_{ij}x_i $$ for $j\in\{1,\dots,n\}$, where $B_{ij}\geq 0$. There is a trivial ...
0
votes
0answers
26 views

How to determine this system of ODE's?

I'm facing this problem: "Suppose you have this system of ODE's: $\begin{pmatrix} \dot y (t)\\ \dot x (t) \end{pmatrix} = \begin{pmatrix} a & b\\ c & d \end{pmatrix} \begin{pmatrix} y (t)\\ ...
1
vote
3answers
19 views

Express last equation of system as sum of multiples of first two equations

The question says to 'Express the last equation of each system as a sum of multiples of the first two equations." System in question being: $ x_1+x_2+x_3=1 $ $ 2x_1-x_2+3x_3=3 $ $ ...
1
vote
2answers
51 views

For which $\lambda$ do we have solutions

I'm trying to find for what values of $\lambda$ the following matrix has either no solutions, infinitely many or unique solutions. $$A=\begin{pmatrix} 1 & 1 & \lambda & 1 \\ 4 & ...
0
votes
1answer
52 views

How do you solve a system of equations with e^x

How do you solve a system of equations with e^x. For example
0
votes
0answers
12 views

Hardness of Solving multivariate quadratic systems

I know that solve multivariate quadratic systems over finite finite fields is a problem NP-Complete, but for instances that can be solved by computers, (e.g. using the F4 algorithm), my doubt is, ...
0
votes
2answers
151 views

Can some inequalities help to pin down an unique solution in a linear system of equations with infinite solutions?

I need to discuss the number of solutions of the following system of equations. Any help would be very appreciated. Consider the known parameters $a_1,...,a_4;d_1,d_2,d_3$ such that $0< a_i< ...
3
votes
0answers
105 views

Solving equation involving factorials

I have this particular equation $\frac{(\alpha-1)!(\beta-1)!}{(\alpha+\beta-1)!} = \frac{\Gamma(p)(1+q)^{n+2p} 2^n}{q^{p}(2+q)^{n+p}}$. Now, given the values of $\alpha$ and $\beta$, I need to find ...
1
vote
0answers
6 views

Closed-form solution for a simple system of concave equations

I am trying to solve what looks like a simple system of equations: $$x_j = A_j\left(\sum_{i=1}^n B_{ij} x_i\right)^\alpha $$ for all $j\in\{1,\dots,n\}$, where $n$ is a positive integer, ...