Question

If xy − log_e y = 1 satisfies the equation \[x\left( y y_2 + y_1^2 \right) - y_2 + \lambda y y_1 = 0\]

 

Options

• −3

• 1

• 3

• none of these

Answer 1

(c) 3

Here,

\[xy - \log_e y = 1\]

\[ \Rightarrow x y_1 + y - \frac{y_1}{y} = 0\]

\[ \Rightarrow xy y_1 + y^2 - y_1 = 0\]

\[ \Rightarrow y y_1 + x y_1 y_1 + xy y_2 + 2y y_1 - y_2 = 0\]

\[ \Rightarrow x\left( {y_1}^2 + y y_2 \right) - y_2 + 3y y_1 = 0\]

\[ \therefore \lambda = 3\]