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Need solution for RD Sharma maths class 12 chapter Differential Equation exercise 21.2 question 15 subquestion (ii)

Answers (1)

Answer:

 2xy\frac{dy}{dx}-(y^{2}+4x^{2})=0

Hint:

 Differentiating the given equation

Given:

 (2x-a)^{2}-y^{2}=a^{2}

Solution:

\begin{aligned} &2(2x-a)2-2y\frac{\mathrm{d} y}{\mathrm{d} x}=0\\ &2x-a=\frac{y}{2}\frac{\mathrm{d} y}{\mathrm{d} x}\\ &a=\left ( 2x-\frac{x}{2}\frac{\mathrm{d} y}{\mathrm{d} x} \right )\\ &\left ( \frac{y}{2}.\frac{\mathrm{d} y}{\mathrm{d} x} \right )^{2}-y^{2}=4x^{2}+\left ( \frac{y}{2}.\frac{\mathrm{d} y}{\mathrm{d} x} \right )^{2}-2.2a.\frac{y}{2}.\frac{\mathrm{d} y}{\mathrm{d} x} \end{aligned}

2xy\frac{dy}{dx}-(y^{2}+4x^{2})=0

Posted by

Gurleen Kaur

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