I'm trying to understand this problem:
The differential equation $\left\{ \begin{align} y'' &= 2x(y − 2)\\ y(0) &= 10\\ y(8) &= 3 \end{align} \right.$ is used with the step $h = 1$. Then an equation system is generated. How many equations does this system have if $y(0)$ and $y(8)$ have been eliminated with help from the boundary conditions?
The correct answer should be 7, but why? Could you explain it? Usually an ODE of order $2$ generates a system of $2$ first-order equation. What is the corresponding rule for boundary value problems?