Verify that the function y = a cos x + b sin x, where, a, b ∈ R is a solution of the differential equation d2y/dx2 + y=0.

Welcome to ASkiitians

The given function is y = a cos x + b sin x … (1)

Differentiating both sides of equation (1) with respect to x,

dy/dx = – a sinx + b cos x

d2y/dx2= – a cos x – b sinx

LHS = d2y/dx2+ y

= – a cos x – b sinx + a cos x + b sin x

= 0

= RHS

Hence, the given function is a solution of the given differential equation.

Thanks