Part $4$: Numerical Techniques $[$total for this section $20\%]$

$($A$)$ Solve the following problems, using Analytical Techniques" and any $3$ suitable

numerical methods $7.$ Compare your analytical method with numerical methods in $0s$

$y10[s].$ In your numerical methods, use time steps of $h=0\mathrm{.}1,0\mathrm{.}01$&$0\mathrm{.}001[s].$

Plot your results on the same figure as much as possible. Comment on the numerical errors. Discuss

the advantages and limitations of both techniques in the context of engineering design.

Part $4($a$)$

i$.y^2+10y-5=0$

ii$.,y^2+10000y-50000=0$