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Applications of Sinusoidal Functions and Their Derivatives

A differential equation is an equation involving a function and one or more of its derivatives. Determine whether the function y=πsinθ+2πcosθ is a solution to the differential equation d^2y/dθ^2 + y = 0

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A differential equation is an equation involving a function and one or more of its derivatives. Determine whether the function y=πsinθ+2πcosθ is a solution to the differential equation d^2y/dθ^2 + y = 0
 
y = nsinθ+2ncosθ
 
y' = ncosθ - 2nsinθ
 
y'' = -nsinθ - 2ncosθ = -(nsinθ + 2ncosθ) = -y
 
Hence
 
y'' + y = -y + y = 0
 
Yes, it is a solution