Consider the following boundary-value problem y" − 2y′ + y = x ^2− 1 , y(0) = 2, y(1) = 4 Apply the linear shooting method and the Euler method with step size of 1/3 to approximate the solution of the problem.

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Question

Consider the following boundary-value problem

$$ y^{\prime \prime}-2 y^{\prime}+y=x^{2}-1, y(0)=2, \quad y(1)=4 $$

Apply the linear shooting method and the Euler method with step size of $\frac{1}{3}$ to marks) approximate the solution of the problem.

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