#### Need solution for RD Sharma maths class 12 chapter Differential Equation exercise 21.2 question 16 subquestion (iii)

The required equation is

$y-2x\frac{\mathrm{d} y}{\mathrm{d} x}=0$

Hint:

The equation is the equation of parabola

Given:

$y^{2}=4ax$

Solution:

$y^{2}=4ax$

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

The required equation is

$y-2x\frac{\mathrm{d} y}{\mathrm{d} x}=0$
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