Problem $3$: The nonlinear model of the Skydiver is given by:

$\frac{dv}{dt}=g-\frac{c}{m}{v}^2$

where $g=9\mathrm{.}81\frac{m}{s^2},c=0\mathrm{.}25k\frac{g}{s},$ and $m=68\mathrm{.}1kg.$

a$.$ Use Euler's Method to derive an approximate solution for the skydiver's velocity

b$.$ Write a MATLAB code $2$ to solve for the approximate solution of the skydiver's velocity at $10$ seconds. Use a $t=2$

c$.$ Plot the exact solution vs$.$ the approximate solution

d$.$ Write a MATLAB code $3$ to solve for the approximate solution of the skydiver's velocity at $10$ seconds. Use a $t=2,1,0\mathrm{.}5,$ and $0\mathrm{.}25.$

e$.$ The code should include the True Percent Error and the Approximate Percent Error values