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jonnejon
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Homework Statement
y'' + 9y = 0 where y(pi/3) = y'(pi/3) = 3
Homework Equations
r^2 + 9 = 0
r^2 = -9
r = 3i
The Attempt at a Solution
y = c1 e^x cos (3x) + c2 e^x sin(3x)
y' = c1 e^x cos (3x) - 3c1 e^x sin (3x) + c2 e^x sin(3x) + 3c2 e^x cos(3x)
y = -c1 e^(pi/3) = 3 => c1 = -3e^(-pi/3)
y' = -c1 e^(pi/3) - 3c2 e^(pi/3) = 3
y' = -(-3e^(-pi/3))e^(pi/3) - 3c2 e^(pi/3) = 3
y' = 3 - 3c2e^(pi/3) = 3 ====> c2 = 0
so
y= -3e^(-pi/3) e^x cos(3x) + 0
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