Question

If y = sin(log x), show that x²y₂ + xy₁ + y = 0.

Answer 1

y = sin(logx) 

y₁ = \(\frac{cos(logx)}{x}\)

xy₁ = cos(log x). 

Again differentiate w.r.t. x 

xy₂ + y₁¹ = \(\frac{-sin(logx)}{x}\)

x²y₂ + xy₁ = -y 

⇒ x²y₂ + xy₁ + y = 0.