I am having trouble solving the following problem:
I have to prove that for the equation $y'''+ (y-5)^2=0$ where $y(t_0)=5$, $y'(t_0)=0$ and $y''(t_0)=0$ where $t \in \Bbb R$, the problem has the unique solution $y(t)=5$. Any ideas for how it can be solved? I just started my MSc so I don't remember much in differential equations.