If y = 3 cos (log x) + 4 sin (log x), prove that x^2y2 + xy1 + = 0.

Question

If y = 3 cos (log x) + 4 sin (log x), prove that x²y₂ + xy₁ + y= 0.

Answer 1

Differentiating with respect to x

[ we can also write this as xy₁ = -3sin(log x ) + 4cos(log x )

Differentiating with respect to x

⇒ x²y₂ = - y - xy₁

⇒ x²y₂ + xy₁ + y = 0

Hence Proved