A second order ODE with one initial condition

Question

Let $F(x , y , y' , y'') = 0$ be the general form of the second order ODE.
I wonder whether it's possible to find a equation in this form such that knowing only one initial condition determines the unique solution.
I mean a degenerate case here in a sense that unique solution is obtained by only one initial condition. Maybe it's possible to construct an equation so that $y\equiv 0$ is the only valid solution but I didn't find anything.