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  • Please solve RD Sharma class 12 chapter Higher Order Derivatives exercise 11.1 question 21 maths textbook solution

Please solve RD Sharma class 12 chapter Higher Order Derivatives exercise 11.1 question 21 maths textbook solution

Answers (1)

Answer:

        Proved

Hint:

You must know about the derivative of exponential function and tangent inverse x

Given:

y=e^{tan^{-1}x},\; \; Prove\: (1+x^{2})y_{2}+(2x-1)y_{1}=0

Solution:

Let\; \; y=e^{tan^{-1}x}

        \begin{aligned} &\frac{d y}{d x}=e^{\tan ^{-1} x} \times \frac{1}{\left(1+x^{2}\right)} \\ &\left(x^{2}+1\right) \frac{d y}{d x}=e^{\operatorname{tan}^{-1} x} \\ &\left(x^{2}+1\right) \frac{d^{2} y}{d x^{2}}+2 x \frac{d y}{d x}=e^{\tan ^{-1} x} \times \frac{1}{\left(1+x^{2}\right)} \end{aligned}

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

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Gurleen Kaur

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