The difference between degree and order of a differential equation that represents the family of cur

Question

The difference between degree and order of a differential equation that represents the family of curves given by $y^{2}=a\left(x+\frac{\sqrt{a}}{2}\right), a>0$ is

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(2) : We have, $y^{2}=a\left(x+\frac{\sqrt{a}}{2}ight)$\ $\Rightarrow \quad 2 y y_{1}=a$\ From (i) and (ii), we get,\ $y^{2}=2 y y_{1}\left(x+\frac{\sqrt{2 y y_{1}}}{2}ight)$\ $\Rightarrow y^{2}-2 x y y_{1}=2^{1 / 2}\left(y y_{1}ight)^{3 / 2}$\ Squaring both sides, we get\ $\left(y^{2}-2 x y y_{1}ight)^{2}=2 y^{3} y_{1}{ }^{3} \Rightarrow\left(y-2 x y_{1}ight)^{2}=2 y y_{1}{ }^{3}$\ $	herefore \quad$ Order $=1$ and degree $=3$\ Required difference $=3-1=2$\