Question

If y = 2 sin x + 3 cos x, then show that y₂ + y = 0.

Answer 1

Given y = 2 sin x + 3 cos x   ....(1)

Differentiating with respect to 'x' we get,

y₁ = 2 cos x - 3 sin x

Differentiating again with respect to 'x' we get,

y₂ = 2 (- sin x) - 3 cos x

y₂ = - 2 sin x - 3 cos x    ....(2)

Adding (1) and (2) we get,

y + y₂ = 2 sin x + 3 cos x - 2 sin x - 3 cos x

= 0 

y + y₂ = 0

Hence proved.