$4.(20$ pts$)$ The free$-$fall velocity of a parachutist can be formulated as

d v$/$d t$=$g$-$c$\_$d$/$m v

where v$=$ velocity $($m $/$ s$),$ t$=$ time $($s$),$ g$=$ acceleration due to gravity $(9\mathrm{.}81$m $/$ s$^2),$ c$\_$d$=$ drag coefficient $(12\mathrm{.}5$kg $/$ m$),$ and m$=$ mass of parachutist $(60$kg$).$ Solve this equation using a$.)(6$ pts$)$ Euler's Method b$.)(6$ pts$)$ Huen's Method$($Special case of $2^$nd Order Runge Kutta's Method c$.)(8$ pts$)$ Plot a graph for the comparison of numerical solutions and exact solution. You must plot results from two different numerical methods and the exact solution in the same Figure$($v$($m$/$s$)$ vs time$($s$)).($Hint: Use dsolve to find exact solution $).$ from t$=0$ to $20$s given that v$(0)=0$ with step size, h$=2.-$ Perform $2$ iterations by hand. $-$ Show your results from first $3$ iterations and last iteration in Table $2$ & $3.($Hint: Use the algorithm given in the class$)$ Table' $2-$ Euler's Method$-$ Perform $2$ iterations by hand. $-$ Show your results from first $3$ iterations and last iteration in Table $2$& $3.($Hint: Use the algorithm given in the class$)$ Tablen $2-$ Euler's Method Table $3-$ Huen's Method