Antiderivatives and Initial Value Problems: Quiz

Problem 4

Find the solution y = y(x) to the initial-value problem

What is y(3)?

Answers, problem 4

y'(x) = 1/x + πcos(πx) + C

We know that y'(2) = 1/2 + π = 1/x + πcos(πx) + C => C = 0

y(x) = ln(|x|) + sin(πx) + D

We know that y(1) = 0 = 0 + 0 + D => D = 0

Therefore y(x) = ln(|x|) + sin(πx)

y(3) = ln(3) = 1.099

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