A linear differential equation is in the form of $a_0(t)y^{(n)} + a_1(t)y^{(n-1)}+ ... + a_n(t)y = g(t)$, and also $a_i(t)$ can be a constant function which is: $a_i(t) = C$.

In this case, $a_1(t) = 0$, so the second derivative $y^{''}$ disappears. However, it's still a linear differential equation.