Answer
$${\text{Two}}$$
Work Step by Step
$$\eqalign{
& y''\left( t \right) + 9y\left( y \right) = 10 \cr
& {\text{The order of a differential equation is the highest order}} \cr
& {\text{appearing on a derivative in the equation}}.{\text{ Therefore,}} \cr
& {\text{This differential equation is second order, then appear }}{\bf{two}} \cr
& {\text{constants in the general solution}}{\text{.}} \cr} $$