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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?

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    Ok the trick is to rewrite y'' with its limit definition but is the answer here really correct since I think it should be 1 instead of 2 at the bottom, since 1²=1 and the formula's here http://en.wikipedia.org/wiki/Second_derivative2012-08-14

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There is one equation at each point. As there are seven points between $0$ and $8$, there are seven equations. The equation at $1$ is $y(2)-2y(1)+y(0)=2\cdot 1(y(1)-2)$. For the other equations, increment the indices of $y$ and make the $1$ the current value of $x$.

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    @NickRosencrantz: You are right, there should not be a 2 in the denominator. Fixed.2012-08-14