\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Consider the following system of non-linear coupled differential equations:$$\begin{cases}\dfrac{dx}{dt} = -x^2 + y \\ \dfrac{dy}{dt} = -(x - y)^2\end{cases}$$
  1. Find the velocity vector \(\begin{pmatrix} \dot{x} \\ \dot{y} \end{pmatrix}\) at the point \((2, 5)\).
    \( \begin{pmatrix}\input{143964}{}{3em}{2em}{}{} \\ \input{243964}{}{3em}{2em}{}{}\end{pmatrix} \)
  2. Find the velocity vector at the point \((1, 0)\).
    \( \begin{pmatrix}\input{343964}{}{3em}{2em}{}{} \\ \input{443964}{}{3em}{2em}{}{}\end{pmatrix} \)