# The differential equation representing the family of curves $\dpi{100} y^{2}=2c(x+\sqrt{c}),\; where \; c> 0,$ is a parameter, is of order and degree as follows Option 1) order 1, degree 1 Option 2) order 1, degree 2 Option 3) order 2, degree 2 Option 4) order 1, degree 3

As we learnt in

Degree of a Differential Equation -

Degree of Highest order differential coefficient appearing in it, provided it can be expressed as a polynomial equation in derivatives

- wherein

$\left ( \frac{dy}{dx} \right )^{2}+3\left ( \frac{dy}{dx} \right )-5=0$

Degree = 2

Degree of a Differential Equation -

Degree of Highest order differential coefficient appearing in it, provided it can be expressed as a polynomial equation in derivatives

- wherein

$\left ( \frac{dy}{dx} \right )^{2}+3\left ( \frac{dy}{dx} \right )-5=0$

Degree = 2

$y^{2}= 2c(x+\sqrt{c})$

$y^{2}= 2cx+2c\sqrt{c})$

$2y.\frac{dy}{dx}=2c$

$\Rightarrow y.\frac{dy}{dx}=c$

$\Rightarrow y^{2}= 2 y\frac{dy}{dx}.x+ 2y(\frac{dy}{dx})^{\frac{3}{2}}$

$\Rightarrow \left(y^{2}- 2x y\frac{dy}{dx} \right )= 2y\left(\frac{dy}{dx}) \right )^{\frac{3}{2}}$

$\Rightarrow \left(y^{2}- 2x y\frac{dy}{dx} \right )^{2}= (2y)^{2}\left(\frac{dy}{dx} \right )^{3}$

order 1, degree 3.

Option 1)

order 1, degree 1

Incorrect option

Option 2)

order 1, degree 2

Incorrect option

Option 3)

order 2, degree 2

Incorrect option

Option 4)

order 1, degree 3

Correct option

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