If y = 3 cos (log x) + 4 sin (log x), show that x² y₂ + xy₁ + y = 0

It is given that y = 3 cos (log x) + 4 sin (log x)

Now, on differentiating we get,

Again differentiating we get,

Therefore,

x² y₂ + xy₁ + y

= -sin(logx) – 7cos(logx) + 4cos(logx) – 3sin(logx) + 3cos(logx) + 4sin(logx)

= 0

So, x² y₂ + xy₁ + y = 0

Hence Proved