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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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