Apply the shooting algorithm to the linear differential equation:

subject to the boundary conditions

For your convenience, use the MATLAB built$-$in function ode$45$ as the stepping algorithm to

move through the differential equation domain from x $=-3$ to x $=-1$

$$ Set the absolute error tolerance to be $10-8$ and a relative error tolerance of $10-10.$

a$)$ Which initial condition is unknown and must be guessed to start the shooting algorithm

$($i$.$e$.$ what is the shooting parameter$)?$

b$)$ What is the residual function for the shooting method in this problem?

$($hint: this residual is not simply moving all terms in the differential equation to one side$)$

$($another hint: this residual is very similar to what the residual from lab $6)$