Consider the following problem.

Solve for $y(t)$ in the ODE below $($Rayleigh$\text{'}$s equation$)$ for $t$ ranging from $0$ to $10$ seconds with

initial conditions $y(0)=5$ and $y^{\text{'}}(0)=0\mathrm{.}1$ and values of mu ranging from $1$ to $10$ in increments

of $1.$

$\frac{d^{2}y}{d{t}^2}-(1-\frac{1}{3}(\frac{dy}{dt}{)}^2)\frac{dy}{dt}+y=0$

Select the methods below that would be appropriate to use for a solution to this problem.

More than one method may be applicable. Select all that apply.

Shooting method

Finite difference method

MATLAB m$-$file euler.m from course notes

MATLAB m$-$file odeRK$4$sys$.$m from course notes

MATLAB function ode$45$

Fourth order centered differencing

Jacobian matrix

MATLAB quad function