Differential equation (Graph the orbit)

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Differential equation (Graph the orbit)

Sinistral
In the  ques below, what do I have to do in part B and E? How do we plot orbits?
Please tell me where to read this from (preferably online) if this is too basic a concept in ODE.
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 "You don't have to believe in God, but you should believe in The Book." -Paul ErdÅ‘s