Question

If y = a cos(log x) + b sin (log x), then

(A) x²(d²y/dx²) + x(dy/dx) + y = 0

(B) x²(d²y/dx²) - x(dy/dx) + y = 0

(C) x²(d²y/dx²) + x(dy/dx) - y = 0

(D) None of these 

Answer 1

Answer is (A) x²(d²y/dx²) + x(dy/dx) + y = 0

y = a cos(log x) + b sin(log x) (1) 

On differentiating Eq. (1) w.r.t. to x both sides, we get