If xy- _ey=1 satisfies the equation x(yy_2+y_1^2)-y_2+ _1=0, then… - Vidyadip

MCQ

If $\text{xy}-\log_\text{e}\text{y}=1$ satisfies the equation $\text{x}(\text{yy}_2+\text{y}_1^2)-\text{y}_2+\lambda\text{yy}_1=0,$ then $\lambda=$

A
$-3$
B
$1$
✓
$3$
D
None of these

✓

Answer

Correct option: C.

$3$

$\text{xy}-\log_\text{e}\text{y}=1$
$\Rightarrow\text{xy}_1+\text{y}-\frac{\text{y}_1}{\text{y}}=0$
$\Rightarrow\text{xyy}_1+\text{y}^2-\text{y}_1=0$
$\Rightarrow\text{yy}_1+\text{xy}_1\text{y}_1+\text{xyy}_2+2\text{yy}_1-\text{y}_2=0$
$\Rightarrow\text{x}(\text{y}_1^2+\text{yy}_2)-\text{y}_2+3\text{yy}_2=0$
$\therefore\lambda=3$

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