The differential equation obtained by eliminating A and B from y = A cos ωt + B sin ωt is
A
Y″ + Y′ = 0
B
Y′ − ω²Y = 0
C
Y″ = −ω²Y
D
Y′ + Y = 0
Correct Option:
C
Explanation
Given Y = A cos ωt + B sin ωt, differentiating twice gives Y″ = −Aω² cos ωt − Bω² sin ωt = −ω²Y. Therefore the differential equation is Y″ = −ω²Y, equivalently Y″ + ω²Y = 0.
