What is Equation system: Definition and 32 Discussions

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought. An equation system is usually classified in the same manner as single equations, namely as a:

System of linear equations,
System of nonlinear equations,
System of bilinear equations,
System of polynomial equations,
System of differential equations, or a
System of difference equations

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  1. R

    A Equation system involving InverseDigamma(Digamma(a+1)-b*k)-1

    How would one go about solving this for a and b given N, E and K? n(0) + n(1) + … + n(K) = N n(0)*0 + n(1)*1 + … + n(K)*K = E Where n(k) = InverseDigamma(Digamma(a+1)-b*k)-1
  2. Nagui

    Finding the Equation System of a Complex Mechanism: Using Lagrange Formalism

    Summary:: equation system of complex mechanism need to be done. Lagrange Formalism could be helpfull to do it but small errors could all destroy .. Hi everyone, I tried to find the equation system of the joined Mechanism (4 DoF). I think there is a mistake but I am not sure where is it . I...
  3. karush

    MHB General Solution of Differential Equation System

    $\tiny{27.1}$ 623 Find a general solution to the system of differential equations $\begin{array}{llrr}\displaystyle \textit{given} &y'_1=\ \ y_1+2y_2\\ &y'_2=3y_1+2y_2\\ \textit{solving } &A=\begin{pmatrix}1 &2\\3 &2\end{pmatrix}\\...
  4. X

    I Take a limit in this 2 equation system of 1st order ODEs

    Hello, I'm having a problem with this system. Ignore the physics. I have the feeling it should be tremendously easy... but I can't figure it out. I don't know how to extract it from the pdf so I'll post just the these 2 pages. https://ufile.io/39ovq The equations are (1.14) and (1.15), the...
  5. T

    MHB Homogeneous, underdetermined equation system

    Hi! Just started with linear algebra Could someone help me with this problem? 2x_1 + x_2 - x_3 + 3x_4 - 3x_5 = 0\\ 3x_1 + 2x_2 + x_3 + 2x_4 + 2x_5 = 0\\ -4x_1 + 3x_2 + 2x_3 + x_4 - 4x_5 = 0 (Sorry, I don't know how to do these big brackets for equation systems in Latex.) So it's a...
  6. Const@ntine

    Comp Sci C++: Method of Minimum Squares used for System Solving

    Homework Statement Okay, this one is a bit big, and I'm attempting a translation, so I'm going to post a TL;DR version at the bottom just to be sure. Anyway, here goes: While doing an experiment, we write down the values of a physical/natural size y, for various values of a physical/natural...
  7. aphirst

    Failure of Optimisation for Nonlinear Equation Systems

    I wasn't sure into which category I should post this, so feel free to move it into a more appropriate place. As part of my work I'm solving a system of nonlinear equations, of a usual form: $$\vec{F}(\vec{X})=\begin{pmatrix}F_1(X_1, X_2, \cdots X_N) \\ F_2(\cdots) \\ \vdots \\...
  8. lucasLima

    Can Newton's Method Solve This Non-Linear System Accurately?

    Homework Statement I'll try to be as clear as possible but this exercise is in portuguese and this is a free translation from me "The sum of two numbers is 3.4 .If we take each of them and summed with they square, the product of it would be 18.5856. The lowest of those number is in the interval...
  9. Rectifier

    Linear algebra - linear equation for a plane

    The problem I am trying to write the equation for the plane on the following form ## ax + by + cz + d = 0 ## $$ \begin{cases} x = 1 + s - t \\ y = 2 - s \\ z = -1 + 2s \end{cases} $$ The attempt ## s, t ## are the parameters for the two directional vectors which "support" the plane. $$...
  10. n7imo

    I Solving a Tricky Nonlinear Equation System: A Quest for Closed Form Solutions

    I'm trying to find a closed form (an algebraic solution) for the following system: x² - y² = 5 x + y = xy It's a bit tricky but I manage to end up with the quartic equation: x^4 - 2x^3 + 5x^2 -10x + 5 =0 And this is where I get stuck looking for a closed form root. Any suggestion would be...
  11. Albert1

    MHB Solve for $a+b+c$: Equation System ($a,b,c\in N$)

    $a,b,c \in N$, and the following equation system is given : $\left\{\begin{matrix} ab+bc+ca+2(a+b+c)=8045-----(1) & & & & \\ abc-a-b-c=-2-----(2) & & & & \end{matrix}\right.$ find the value of $a+b+c$
  12. B

    MATLAB How to calculate equation system in Matlab, with some knowns

    It's part of finite elements analysis. All I need is to solve F=Ku,K is [12x12] matrix . Some of the members of u are zeros ,some members of F are known forces . K is all known . How do I solve F=Ku in that way ?? Thanks in advance.
  13. Albert1

    MHB Find the solution of the equation system

    find the solution of the equation system: $\begin{cases} a=\dfrac{b+c+d}{3}---(1)\\ b=\dfrac{a+c+d}{5}---(2)\\ c=\dfrac{a+b+d}{7}---(3)\\ d=c+5600\,\, ---(4)\end{cases}$ here $a,b,c,d>0$
  14. M

    MHB Find equation system for boundary value problem

    For $\Omega = (0,1)^2 \subseteq \mathbb R^2, f \in C(\Omega)$ consider the boundary value problem: $-\Delta u(x,y) + u(x,y) = f(x,y)~ \forall (x,y) \in \Omega \\u(0,y) = u(1,y)~ \forall y \in (0,1) \\ u(x,0) = u(x,1)~ \forall x \in (0,1)$ For discretization let be: $n \in \mathbb N,~ h=...
  15. Maxo

    How to Solve an Equation System with Substitution Method?

    Homework Statement v_{f1}^2 = v_{01}^2 - m_{1}/m_{2} * v_{f2}^2\\ v_{f2} = m_{1}/m_{2} * (v_{01} - v_{f1}) Solve for Vf1 algebraically. How to solve this in the easiest way without having miles of calculations? Homework Equations The Attempt at a Solution When I try to use the...
  16. P

    Differental equation system and Lyapunov stability

    Homework Statement Example: x'=y-x^3 y'=-x-y^3 Homework Equations The Attempt at a Solution Linear system x'=y y'=-x Is stable because Det(P-\lambdaE)=\lambda2+1 \lambda1,2=+-i So if I am not mistaken,than Ishould use Lyapunov stability,because the linear system is stable and I can't say...
  17. L

    Nonlinear coupled differential equation system - kinetics

    Dear All, Recently, I have measured a series of nonlinear vibrational spectra from which I would like to extract some useful information about kinetics of the exchange process occurring in the studied system. I need to fit my experimental data to kinetic model that is a solution of coupled...
  18. T

    Differential Equation system and matrix

    I have a quick question. I have to write the differential equations in matrix form Eq1:= x1'(t) = -a1*x1(t) + vf Eq2:= x2'(t) = a1*x1(t) - a2*x2(t) is this correct :
  19. T

    Problem solving equation system

    Homework Statement Solve this equation system for x, y and lambda. \left\{\begin{matrix} 2x = \lambda (2x-6y)\\ 2y = \lambda(-6x-14y)\\ x^2-6xy-7y^2+80=0 \end{matrix}\right. The Attempt at a Solution I really tried A LOT of things, but I can't solve it. I think it is not helpful to post...
  20. D

    Linear Algebra: Linear Equation System -> Parameter Form

    Homework Statement Consider the following linear system of equations: x1+2x3-5x4 = 0 x1 + 4x2 +4x3 – 5x4 = 10 x1 + 2x2 + 3x3 – 5x4 = 5 4x1 + 2x2 + 9x3 – 20x4 = 5 b) Solve the equation system with the Gaussian method. c) The solution set describes a plane. Specify it in the parameter...
  21. M

    Shallow water flow - equation system unstable

    Hello, everyone. I'm working on simulating shallow water flow. I'm using the MacCormack scheme and fractional predictor-corrector steps. The Dxy factor should make the equation system stable but no matter what numbers I input, the results skyrocket, up to 10^80 and more. Has anyone worked...
  22. E

    Finding the Product of Primes: A Number Theory Puzzle

    Hi i found a question in number theory, involving two equations, it goes as follows: Let p1, p2, p3 and p4 be 4 different prime numbers satisfying the equations 2p1 + 3p2 + 5p3 + 7p4 = 162 11p1 + 7p2 + 5p3 + 4p4 = 162 Find all possible values of p1p2p3p4. Not knowing what to do, i used the...
  23. S

    Solving Differential Equation System

    Homework Statement x`=z-y y`=z z`=z-x x(0)=1; y(0)=1; z(0)=1 The Attempt at a Solution Would be glad to know the steps I need to take.
  24. Y

    How to deal with homogenous differential equation system?

    How to deal with homogenous differential equation system?? Homework Statement s'[t] == (-3 s[t])/580, m'[t] == (-19 m[t])/590, h'[t] == (3 s[t])/580 + (19 m[t])/590 - (2 h[t])/25, e'[t] == (2 h[t])/25 - (85 e[t])/116, o'[t] == (85 e[t])/116 - (33 o[t])/131 Homework Equations it...
  25. M

    Solving equation system, need to augment my code

    Hello, friends. I just registered because I desperately need some help. Homework Statement For my bachelor's degree in physics, I'm trying to simulate gravitational microlensing of a background source on a system of objects, acting as gravitational lenses. I have the equation up and running...
  26. C

    Ordinary Differential Equation System with Variable Coefficients

    Homework Statement For t\in\mathbb{R}, let: A=\left[\begin{array}{ccc} -1 & 0 & 0\\ 0 & 2 & 2t\\ 0 & 0 & 2\end{array}\right] Get the solution for the general equation: X'=A(t)X Homework Equations The Attempt at a Solution I done many of these problems, all with constant...
  27. E

    Solve a Integer equation system

    Find smallest d=2a^2=3b^3+2=5c^5+3 where a,b,c are integers. This problem is very hard. Either no solution or d is toooooooo big
  28. M

    General solution of differential equation system

    Homework Statement Find the general solution of the system of differential equations x'=10x - 12y y'=25x - 30y (where primes indicate derivatives with respect to t) by using the initial conditions x(0)=A y(0)=B Homework Equations The Attempt at a Solution x''=10x' - 12y'...
  29. D

    Matrix equation system

    given the matrix A and vectors X & B A= 1 2 3 2 k 6 0 0 k-4 k 2k 3k X= x1 x2 x3 B= 2 4 0 2k what values of K(if any) will give AX=B-- a) with no possible x1 x2 x3 b) with a single x1 x2 x3, what are they c) with infinite options, including 1 free parameter? what is this...
  30. M

    Python, RungeKutta and first-order differential equation system.

    [b] Homework Equations The equation is, given to me by lurflurf,: mv' + f(v ) + s(u) = F(t), t > 0, u(0) = U0, v (0) = V0 where v=u' For the record the equation was: mu'' + f(u' ) + s(u) = F(t), t > 0, u(0) = U0, u' (0) = V0 . The Attempt at a Solution def rhs(u, t)...
  31. D

    How to Solve a Cubic System by Eliminating Variables?

    x³+y³=1 x²y+2xy²+y³=2
  32. R

    Differential equation system, got stuck in a physics problem

    hi guys, I'm solving a pretty complex problem: calculating a trajectory of a charged particle in a custom magnetic field. I arrive to the point where this very nice equation system blocks my way :P http://ramses728.altervista.org/img/phys.jpg hope you can help me somehow
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