Question

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... ​

Answer 1

Answer:

Y= a cosx + b sinx

dy/dx = - a sinx +b cosx

d2y/dx2= - a cos x - b sinx

LHS

d2y/dx= - a cosx - b sinx

LHS =d2y/dx2 +y

=. - a cosx - b sinx +a cosx + b sinx

=0

= RHS

HENCE, Verified

Answer 2

refer the attachment :)