Question

The differential equation of minimum order by eliminating the arbitrary constants A and C in the equation y = A[sin(x + C)+ cos(x + C)] is 

A. y"+ (sinx + cosx)y′ = 1 

B. y" = (sinx + cosx)y′ 

C. y" = (y′)² + sinx cosx

D. y"+ y = 0

Answer 1

Correct option D. y"+ y = 0

Explanation:

y = A [sin(x+c) + cos(x+c)] 

y’ = A [cos(x+c) – sin(x+c)] 

y’’ = -A [sin(x+c) + cos(x+c)] = -y 

or y’’ + y = 0