# 2

1. ### Differential equation #2#

y'-xy''-\frac{1}{y'' }=0.
2. ### How to prove that $2$ is an irreducible element in $\mathbb {Z}[\sqrt{5}]$?

How to prove that $2$ is an irreducible element in $\mathbb {Z}[\sqrt{5}]$? One way is to check if there exists $a,b,c,d \in \mathbb Z$ such that $2=(a+b\sqrt{5})(c+d\sqrt{5})$, i.e., $2=ac+ 5bd+ \sqrt{5}(ad+bc)$. It leads to the system $ac+5bd=2$ and $ad+bc=0$, which is difficult to solve. Is...