The differential equation representing the family of curves $y^{2} = 2c(x + c^{\frac{2}{3}})$, where $c$ is a positive parameter, is of

Question

Dr. Abubacker · Accepted Answer

(c)
$y^{2} = 2c(x + c^{\frac{2}{3}})$
$\Rightarrow$ $2y\ \frac{dy}{dx} = 2c \Rightarrow c = y\ \frac{dy}{dx}$
$	herefore$ $y^{2} = 2y\ \frac{dy}{dx}\left( x + \left( y\ \frac{dy}{dx} ight)^{\frac{2}{3}} ight)$
$\Rightarrow$ $\left( \frac{y}{2\frac{dy}{dx}} - x ight) = \left( y\ \frac{dy}{dx} ight)^{\frac{2}{3}}$
$\Rightarrow$ $\left( y - 2x\ \frac{dy}{dx} ight)^{3} = \left( 2\ \frac{dy}{dx} ight)^{3}\left( y\ \frac{dy}{dx} ight)^{2}$
$\Rightarrow$ $\left( y - 2x\ \frac{dy}{dx} ight)^{3} = 8y^{2}\left( \frac{dy}{dx} ight)^{5}$
Here, order=1, degree=5

Q. The differential equation representing the family of curves $y^{2} = 2c(x + c^{\frac{2}{3}})$, where $c$ is a positive parameter, is of

Explanation

Reviewed by Dr. Abubacker

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