# Tagged Questions

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### Solving system of equations

I have the following set of equations: $y = f(a,b)$ $a = f(y)$ $\dot{b} = f(b,y,\dot{y})$ which I like to solve for $y$. I was wondering if there is some numerical method which I can apply to ...
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### 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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### 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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### 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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### 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 ...
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### 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 ...
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### 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 ...
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### Solving solely continuous system of ode's with matlab

I'm working with the numerical integration of the system of differential equations, $\dot{x}=f(x)$ with the vectorfield, $f(x)$ being solely continuous. Examples of the systems which I'm working on ...
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### Need help with simple system of differential equations

thanks to your help I advanced in computing differential equations, but now I encountered another problem I need help with - this time it is a system of differential equations: $$x_1'=-x_2$$ ...
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### How to express $z'(t)$ and $w'(t)$ in terms of $z(t)$ and $w(t)$?

I have these functions: $x' (t) = −5x(t) + 2 y(t)$ $y' (t) = 2x(t) − 2y(t)$ where $x(0)=10$ and $y(0)=0$ I am also given these 2 functions: $z(t) = x(t) + 2y(t)$ $w(t) = −2x(t) + y(t)$ First ...
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### Solving a system of linear ODEs

Based on my previous post, I have been stuck on this for a few hours now. I want to solve for $x$ and $y$ from the equation $$\frac{dx}{dt} + \frac{dy}{dt}=a-(b+c+d)y-bx.$$ The original two equations ...
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