Consider an eigenvalue problem

$y^{\text{'}\text{'}}(x)+y(x)=0,y(0)=0,y(1)=0$

a $[5$ marks$]$ Find the exact representation for the eigenvalues of $(6)$ and the coresponding

eigenfunctions. What is the range for values of $?$

b $[10$ marks$]$ Write the Python code to implement the shooting method based on RK$4$

with the parameter $$ from the obtained range to find such approximate solutions so you

can apply the bisection method$\mathrm{.}3.$ Consider an eigenvalue problem

y

$($x$)+\backslash$lambda y$($x$)=0,$ y$(0)=0,$ y$(1)=0(6)$

a $[5$ marks$]$ Find the exact representation for the eigenvalues of $(6)$ and the coresponding

eigenfunctions. What is the range for values of $\backslash$lambda $?$

b $[10$ marks$]$ Write the Python code to implement the shooting method based on RK$4$

with the parameter $\backslash$lambda from the obtained range to find such approximate solutions so you

can apply the bisection method.