Tutorial_1

Tutorial_1 - Tutorial 1 Question 1 A cup of coffee has...

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Unformatted text preview: Tutorial 1 Question 1 A cup of coffee has temperature vs. time . Assume the temperature drops according to Newton’s law of cooling: =− − = 20℃ 0 = 80℃ where is a constant, say = 0.1 coffee has an initial temperature of is the constant room temperature, say . 0 = 80℃. Predict . = 20℃. The (a) Are the units consistent between the right side and left side of the ODE? (b) Solve the ODE. Question 2 ODE: + −2 =0 0 =1 BCs: 2 =3 for 0 ≤ Find ≤ 2. Question 3 ODE: +4 =5 0 =0 ICs: ′ 0 =0 Find: Question 4 Using the method of Frobenius, find the first three terms in the series expansion about general solution to the following ODE: 9 +9 +2 =0 for >0 = 0 for a ...
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