4.180. $\frac{d x}{d t}=x-y, \frac{d y}{d t}=x+y$.
Solution. We form the characteristic equation

$$
\left|\begin{array}{cc}
(1-\lambda) & -1 \\
1 & (1-\lambda)
\end{array}\right|=\lambda^{2}-2 \lambda+2=0
$$

The roots of the characteristic equation are complex conjugates, with a positive real part and a non-zero imaginary part:

$$
\lambda_{1,2}=1 \pm i (\text{case } 2 \mathrm{~b}: \alpha=1>0, \beta=1 \neq 0).
$$

The equilibrium point is an unstable focus.