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  • Please solve RD Sharma class 12 chapter Differential Equation exercise 21.2 question 14 maths textbook solution

Please solve RD Sharma class 12 chapter Differential Equation exercise 21.2 question 14 maths textbook solution

Answers (1)

Answer:

 \frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}(1-x^{2})-\frac{\mathrm{d} y}{\mathrm{d} x}x-2=0

Hint:

 Differentiating the given equation with respect to x

Given:

 y=(sin^{-1}x)^{2}+A\, cos^{-1}x+B

Solution:

\begin{aligned} &\frac{\mathrm{d} y}{\mathrm{d} x}=2sin^{-1}x\frac{1}{\sqrt{1-x^{2}}}+A\left ( \frac{-1}{\sqrt{1-x^{2}}} \right )+0\\ &y'=\frac{1}{\sqrt{1-x^{2}}}\left [ 2sin^{-1}x-A \right ]\\ &y'\sqrt{1-x^{2}}=2sin^{-1}x-A\\ &A=2sin^{-1}x-y^{2}\sqrt{1-x^{2}} \end{aligned}

\begin{aligned} &0=\frac{2}{\sqrt{1-x^{2}}}-y''\sqrt{1-x^{2}}-y^{2}\frac{1(-2x)}{2\sqrt{1-x^{2}}}\\ &0=\frac{2}{\sqrt{1-x^{2}}}-y''\sqrt{1-x^{2}}+\frac{y^{2}x}{\sqrt{1-x^{2}}}\\ &0=\frac{2-y''(1-x^{2})+y^{3}x}{\sqrt{1-x^{2}}} \end{aligned}

\begin{aligned} &y''(1-x^{2})-y'x-2=0 \end{aligned}

\frac{\mathrm{d} ^{2}y}{\mathrm{d} x^{2}}(1-x^{2})-\frac{\mathrm{d} y}{\mathrm{d} x}x-2=0

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Gurleen Kaur

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