Using one of the Newton$$s method codes we$$ve built in class, solve the following system

of nonlinear equations and submit the solutions in a text document $($word or PDF$)$ and

your m file:

xy$5$ y $=10$

y$2=3$ x$3+6$

$2.*$From Introduction to Numerical Methods and MATLAB for Engineers by Todd Young

and Martin J$.$ Mohlenkamp$*($Lecture #$29)$:

Solve the following differential equation by first reducing it into a system of first order

ODE$$s then using ode$45$ to solve it in MATLAB. Submit your m file and plot of x vs$.$ t

from t $=1$ to t $=2($i$.$e$.,[1,2]).$ Use initial guesses of x$(1)=1,$x$(1)=2,$ and $$x$(1)=0.$

$($Hint: plot only one resulting equation at a time and remember which one is x vs$.$ t$...$ do

not submit plots of the derivative functions$).$

$$

x $+$x$23$x$3+$cos$2($ x $)=$e$$t sin $(3$t $)$

You must submit your $.$m files for problems $1$ and $2.$

Also please write out your solutions for each problem on paper and take a photo or type

them into a word document.

Notes:

$$ Use the following file naming convention: lastname$\_$HW$6$ for submission files

$**$Grading: Each problem is worth $5$ points