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1. Use Euler’s method with step size ∆x = 1 to approximate y(4), where y(x) is...

1. Use Euler’s method with step size ∆x = 1 to approximate y(4), where y(x) is the solution of the initial value problem:

y' = x2+ xy

y(0) = 1

2. The coroner arrives at a murder scene at 9:00 pm. He immediately determines that the temperature of the body is 83◦F. He waits one hour and takes the temperature of the body again; it is 81◦F. The room temperature is 68◦F. When was the murder committed? Assume the man died with a body temperature 98◦F. (Hint: Newton’s Law of Cooling)

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