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If `x y-(log)_e y=1` satisfies the equation `x(y y_2+y1 2)-y_2+lambday y_1=0,t h e nlambda=` `-3` (b) 1 (c) 3 (d) none of these

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`x y-log _{e} y=1`
` Rightarrow x y_{1}+y-frac{y_{1}}{y}=0`
` Rightarrow x y_{1}+y^{2}-y_{1}=0`
` Rightarrow y y_{1}+x y_{1} y_{1}+x y_{2}+2 y_{1}-y_{2}=0`
` Rightarrow x(y_{1}^{2}+y_{2})-y_{2}+3 y_{1}=0`
` therefore lambda=3`
`
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