$If y = a c o s (l o g x) + b s i n (l o g x) t h e n x^{2} y_{2} + x y_{1} =$

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-y

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Solution

The correct option is D
-y

$y = a c o s l o g x + b s i n l o g x \Rightarrow y_{1} = \frac{- a s i n l o g x + b c o s l o g x}{x} \Rightarrow x y_{1} = - a s i n l o g x + b c o s l o g x \Rightarrow y_{1} + x y_{2} = \frac{- a c o s l o g x - b s i n l o g x}{x} \Rightarrow x y_{1} + x^{2} y_{2} = - y$

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