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asdf.
The incorporation of the boundary conditions yield two additional equations. -1 point
b. We know that $y(x)= c_1 x^1 + c_2 x^2 \ldots C_{N+1}x^{N+1} $. We also have $y''(x) = 2c_2 +6c_3 \ldots N(N+1)c_{N+1}X^{N-1} $
We have $y(0) = y(1) = 0.$ We can say that $ c_0 =0 $ and $c_1 +c_2 + \ldots C_{N+1}$. From the equation given we have $y''(x) -\exp (y(x)) =0.$ We can evaluate each N equation at each grid points: We have the following: we have $h = \frac{1}{N+1}$
$$ 2 c_2 + 6 c_3 h + \ldots N(N-1)c_{N+1} h^{(N-1)} - [\exp(c_1 h^1 + c_2 h^2 \ldots C_{N+1}h^{N+1}]$$
$$\vdots $$
$$ 2 c_2 + c_3 Nh + \ldots N(N-1)c_{N+1} {Nh}^{(N-1)} - [\exp(c_1 Nh + c_2 {Nh}^2 \ldots C_{N+1}{Nh}^{N+1}] $$
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