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  • Please solve RD Sharma class 12 chapter Differential Equation exercise 21.2 question 16 subquestion (v) maths textbook solution

Please solve RD Sharma class 12 chapter Differential Equation exercise 21.2 question 16 subquestion (v) maths textbook solution

Answers (1)

Answer:

 The required differential equation is

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

Hint:

 Differentiating equation (i) with respect to x

Given:

 (x-a)^{2}-y^{2}=1

Solution:

The equation of family of curves is

(x-a)^{2}-y^{2}=1 \qquad \qquad \dots(i)

Where a is a parameter

Differentiating equation (i) with respect to x, we get

\begin{aligned} &2(x-a)-2y\frac{\mathrm{d} y}{\mathrm{d} x}=0\\ &(x-a)-y\frac{\mathrm{d} y}{\mathrm{d} x}=0\\ &\sqrt{1+y^{2}}=y\frac{\mathrm{d} y}{\mathrm{d} x} \qquad \qquad [U\! sing (i)]\\ &(1+y^{2})=y^{2}\left ( \frac{\mathrm{d} y}{\mathrm{d} x} \right )^{2} \end{aligned}

 The required equation is

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

Posted by

Gurleen Kaur

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