Problem Sheet 6 - Boundary Value Problems

1. Consider the boundary value problem

(556)$$y^{″}=3x{y}^{\prime }-4y+x^2,1\le x\le 2,y(1)=2,y(2)=-1.$$

Apply the linear shooting method to transform this equation into two second order initial value problems
and approximate the solution using the Euler method with stepsize $h=\frac{1}{3}.$