Use example $22\mathrm{.}1$ on page $556$ of your text to explore solving first order ordinary

differential equations $($also given on second page of this assignment$).$

a$.$ Is the differential equation linear or non$-$linear?

b$.$ Write a script that will solve the first order ordinary differential

numerically using Euler$$s method. Use the script to recreate table $22\mathrm{.}1.$

c$.$ Half the time step and create the resulting table similar to table $22\mathrm{.}1.$

d$.$ Solve the ODE in the example with the Fourth Order Runge$-$Kutta method

given on page $495$ in your text. Create tables similar to those created in b

and c for this method. Discuss the impact on the error of halving the time

step for each method.

e$.$ Solve the same differential equation with ode$45.$