I am dealing a little hastily with some texts on ODE's and did not understand the following. A professor had a 3ª order ODE and suggest factorate at form:
$$(D^2+p_1(x)D+p_2(x))(D+p_3(x))y(x)=0,$$ where $D=d/dx$.
He said that $(D+p_3(x))\overline{y}(x)=0$ for a solution $\overline{y}$. I ask why?
I could not understand...
Many thanks in advance!