# Solve the Cauchy Problem: $y' = f(x,y), y(x_0)=y_0$ where $f(x,y) = Ly+ \delta$, $L, \delta \in \mathbb{R}_{>0}$

I want to understand the solution sheet to the following question : Solve the cauchy problem: $y' = f(x,y), y(x_0)=y_0$ where $f(x,y) = Ly+ \delta$, $L, \delta \in \mathbb{R}_{>0}$

The solution says there are two possible cases:$y_0 = -\dfrac{\delta}{L}$ and $y_0 \neq -\dfrac{\delta}{L}$

I understand the second case but for the first case i.e. $y_0 = -\dfrac{\delta}{L}$ they say the following (which I don't understand):