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  • Need solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 31

Need solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 31

Answers (1)

Answer:

Proved

Hint:

You must know the derivative of exponential function

Given:

y=a e^{2 x}+b e^{-x}, \text { show } \frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}-2 y=0

Solution:

y=a e^{2 x}+b e^{-x}

        \begin{aligned} &\text { Differentiate the equation w.r.t } x\\ &\frac{d y}{d x}=2 a e^{2 x}+b e^{-x}\\ &\frac{d^{2} y}{d x^{2}}=4 a e^{2 x}+b e^{-x} \end{aligned}

        \begin{aligned} &\text { LHS }=\frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}-2 y \\ &=4 a e^{2 x}+b e^{-x}-2 a e^{2 x}+b e^{-x} \\ &=-2 a e^{2 x}-2 b e^{2 x} \\ &=0=\text { RHS } \end{aligned}

Posted by

Gurleen Kaur

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