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  • Please Solve RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Questions Maths Textbook Solution Question 25

Please Solve RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Questions Maths Textbook Solution Question 25

Answers (1)

Answer:              

(c)

Hint:

We must know about the derivative of logarithm.

Given:

                x y-\log _{e} y=1 \\   satisfy the equation  x\left(y y_{2}+y_{1}^{2}\right)-y_{2}+\lambda y y_{1}=0

Explanation:

                x y-\log _{e} y=1 \\

                \begin{aligned} & &x y_{1}+y-\frac{y_{1}}{y}=0 \end{aligned}

                \frac{x y y_{1}+y^{2}-y_{1}}{y}=0

                \begin{aligned} &\\ &x y y_{1}+y^{2}-y_{1}=0 \end{aligned}

                y y_{1}+x y_{1} y_{1}+x y y_{2}+2 y y_{1}-y_{2}=0 \\

                \begin{aligned} & &x\left(y_{1}^{2}+y y_{2}\right)-y_{2}+3 y y_{1}=0 \end{aligned}

Compare with given equation,

                x\left(y y_{2}+y_{1}^{2}\right)-y_{2}+\lambda y y_{1}=0

                \begin{aligned} & \\ &\lambda=3 \end{aligned}

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