Applications of Sinusoidal Functions and Their Derivatives

Question

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

Answer 1

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