Consider again the second$-$order ordinary differential equation given in Eq$.(1),$ that is$,$

x$($t$)+\backslash$omega $2$

nx$($t$)=0.(2)$

For this problem, the solution to the differential equation in Eq$.(2)$ will be obtained in a manner

different from that of Question $1.$ First, show the following relationship:

x$=$ x$$

dx$$

dx $.(3)$

Rewrite Eq$.(2)$ using the relationship of Eq$.(3).$ Solve the transformed version of Eq$.(3)$ for x$$ as a

function of x using the initial conditions $($x$(0),$ x$(0))=($x$0,$ v$0).$ Plot the solution x$$ as a function of

x for the following initial conditions:

$($a$)($x$(0),$ x$(0))=($x$0,$ v$0)=(1,0).$

$($b$)($x$(0),$ x$(0))=($x$0,$ v$0)=(0,1).$

Make a single plot that captures both sets of initial conditions given in $($a$)$ and $($b$).$ Use the MATLAB

legend command to label each plot with the appropriate set of initial conditions.