Order and Degree of a Differential Equation

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The differential equation representing the family of curves $y^{2} = 2 c (x + c)$ , where $c > 0$ , is a parameter, is of order and degree as follows :

order 1, degree 2

order 1, degree 1

order 1, degree 3

order 2, degree 2

The degree and order of the differential equation of the family of all parabolas whose axis is $x$ -axis, are respectively.

The order and degree of the differential equation $(1 + 3 \frac{d y}{d x})^{2/3} = 4 \frac{d ^{3} y}{d x ^{3}}$ are

(1, \frac{2}{3})

(3, 1)

(3, 3)

(1, 2)

JEE Advanced 1998

The order of the differential equation whose general solution is given by $y = (C_{1} + C_{2}) cos (x + C_{3}) - C_{4} e^{x + C_{5}}$ , where $C_{1}, C_{2}, C_{3}, C_{4}, C_{5}$ are arbitrary constants, is

JEE Main 2021 (February)

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