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Questions tagged [nonlinear-system]

In mathematics, a nonlinear system of equations is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one.

In mathematics, a nonlinear system of equations is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. Reference: Wikipedia.

In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the unknown variables or functions that appear in it (them).

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Solving equation: non-linear

I am trying to find the values of x, y and z having these equations. a, b and c are constants. $$ \begin{cases} a = (\frac y x)^{1/2} \cdot \frac {x+y} x \\ b = (\frac z x)^{1/2} \cdot \frac {z+x} x \\ c = (\frac y z)^{1/2} \cdot \frac {y+z}…
Pro
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Solving equation with matrices fraction

Im trying to solve this equation with respect to $m$ which is a $K×1$…
tata
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How to solve a system of nonlinear equations?

How can one solve this system of equations: $$ \begin{align} x(t) = a \cos(\omega t + \phi) + \dfrac{\beta a^3}{32} \cos(3(\omega t + \phi)), \\ p(t) = -a \omega \sin(\omega t + \phi) - 3 \omega \dfrac{\beta a^3}{32} \sin(3(\omega t +…
Andrew Semyonov
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Analytical solution to a nonlinear equation

I have a hard time finding the analytical solution to the following non-linear equation: $$ (1+x)^{1-p} + p^{\frac{p}{1-p}}x(p-1) - 1 = 0 $$ where $p \in ]0,1[$ and $x > 1$. I would like to have a solution $x$ in terms of $p$ for each fixed $p$ in…
infinite_monkey
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Solve the following system

Solve the following system in $$x, y, z$$ : $$2 ^ x 3 ^ y 5 ^ z = 2 ^ y 3 ^ z 5 ^ x = 2 ^ z 3 ^ x 5 ^ y = 30$$ I have tried to solve it but it seems impossible to solve.
Anonymus
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When a solution of a non-linear system exist?

I was trying to solve a problem and end up with the following non-linear system $$\left\{\begin{array}{lll} a_{11}e^{x_1}+ \ldots+…
A.K.O
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Method to solve a system of nonlinear equations

Suppose that I have the following system, $$ \begin{equation} \left\{\begin{array}{lcl} a + b + c + d & = & \alpha \\ a^2 + b^2 + c^2 + d^2 & = & \beta \\ a^3 + b^3 + c^3 + d^3& = & \gamma \\ a^4 + b^4 + c^4 + d^4& = & \theta …
Odds'n'Ends
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Fixed points of $g$?

Consider the functions $f(x) = 1 - \frac{1}{2x}$ and $g(x) = 2x(1-x)$ How many roots does $f$ have? Are the roots of $f$ fixed-points of $G$ are there more fixed points of $g$ than roots of $f$? Confused as to how to answer this question The roots…
ss sss
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How to solve equations of type $a*x^c+b*x^d-S==0$?

How to solve the following equation $$ a*x^c+b*x^d-S==0 $$ for $x$. Wolfram alpha and sympy are not able to solve this. Any suggestions?
OD IUM
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Rewrite nonlinear equation system

Is there anyway to rewrite this system to a system of $Q_1$,$Q_2$,$Q_3$ and $Q_4$ instead? $a,b,c,d,m$ are real numbers. $$\begin{align} a&=Q_1^2-Q_2^2-Q_3^2+Q_4^2+m\\ b&=2Q_1Q_2-2Q_3Q_4\\ c&=2Q_1Q_3+2Q_2Q_4\\ …
Linus
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Is there a closed solution to the following differential equation?

I've just encountered the following differential equation in a design problem $\dot{l}\cos \theta - \dot{\theta}l \sin \theta = A[\dfrac{1}{\sqrt{r}}-\dfrac{1}{\sqrt{r+l\sin \theta}}] \quad (*)$. Here $A$ and $r$ are constant parameters. Regarding…
user240612
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nonlinear equation

Is there any way other than symbolic tool, to solve for nonlinear set of equations in MATLAB without initial condition? (Symbolic tool doesn't work or is very time consuming for very high order system of nonlinear equations)
Navid Hashemi
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Solve $\ln(1-x)-\ln(x)+\frac{a}{x}=c$ for $x$

Is there an analytical (maybe involving special functions) solution of an equation of the form: $$\ln(1-x)-\ln(x)+\frac{a}{x}=c$$ Here I want to solve for $x$, which should satisfy $0\le x\le1$, and $a,c$ are real constants.
a06e
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What does the lack of singular points of non liniar system mean in phase portraits?

I'm going to plot the phase portrait of this system: $\dfrac{dx}{dt}=-x^2 + 4 y^2$ $\dfrac{dy}{dt}=-8 - 4 y + 2 x y$ The singular point $(x,y)$ can be found from the system: $-x^2 + 4 y^2=0$ $-8 - 4 y + 2 x y=0$ Seems this system doesn't have roots…
Stdugnd4ikbd
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Prove that no periodic orbits exist

Please help! I need to prove for the system below that no periodic orbits exist when $V_0=0$: $\frac{d^2x}{dt^2}+\zeta_1 \frac{dx}{dt}+(k_{11}+k_{12}x^2)x-2\gamma\frac{dy}{dt}=V_0 cos(\omega t),$ $\frac{d^2y}{dt^2}+\zeta_2…
Dennis
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