Why can't a second order differential equation have 2 Neuman conditions? I read that a problem such as:
\begin{equation}
    \begin{cases}
       -\frac{\partial^2 y}{\partial x^2} + y = f(x)\\
       \mathrm{condition} \ n°1\\
       \mathrm{condition}  \ n°2
    \end{cases}
\end{equation}
Could have a unique solution if $\mathrm{condition} \ 1$ and $\mathrm{condition} \ 2$ were:

*

*Initial conditions (Cauchy problem)

*2 Dirichlet conditions ($y(a) = y_a, \ y(b) = y_b \ | \ b > a, \ x \in [a, b]$)

*1 Dirichlet condition + 1 Neuman condition ($y'(a) = y_a, \ y(b) = y_b \ | \ b > a, \ x \in [a, b]$ or the contrary)

Why can't we have 2 Neuman conditions ?

Because you can’t have all your conditions with derivates. You need at least 1 normal condition because of the integration constant.
