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Problem 15 - Entrance Test

An Algerian satellite orbits such that its distance from planet center satisfies r″–4r=0, r(0)=3, r′(0)=6. What is r(t)?

Correct: A

General solution r=Ae^(2t)+Be^(–2t). Initial: A+B=3, 2A–2B=6 ⇒ A=3, B=0 ⇒ r=3e^(2t).