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  • Please Solve RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Questions Maths Textbook Solution Question 27

Please Solve RD Sharma Class 12 Chapter 11 Higher Order Derivatives Exercise Multiple Choice Questions Maths Textbook Solution Question 27

Answers (1)

Answer:

                (a)

Hint:

We must know about the derivative rules of exponential functions.

Given:

                y=A e^{5 x}+B e^{-5 x} \\

Explanation:

                y=A e^{5 x}+B e^{-5 x} \\

                \frac{d y}{d x}=A e^{5 x} \cdot 5+B e^{-5 x} \cdot(-5) \\

                \begin{aligned} & &\frac{d y}{d x}=5 A e^{5 x}-5 B e^{-5 x} \end{aligned}

Again differentiate with respect to  x

                \frac{d^{2} y}{d x^{2}}=5 A e^{5 x}(5)-5 B e^{-5 x}(-5) \\

                \begin{aligned} & &\frac{d^{2} y}{d x^{2}}=25 A e^{5 x}+25 B e^{-5 x} \end{aligned}

                \frac{d^{2} y}{d x^{2}}=25\left[A e^{5 x}+B e^{-5 x}\right] \

                \begin{aligned} &\ &\frac{d^{2} y}{d x^{2}}=25 y \end{aligned}

 

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