Question

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

• A. Order 1
• B. Order 2
• C. Degree 3
• D. Degree 4

Answer 1

Answer: (C)

Degree 3

Answer 2

We have, $y^{2} = 2c\left( x + \sqrt{c} \right)$

⇒ $2yy_{1} = 2c$

⇒ $yy_{1} = c$

⇒ $c = \frac{y}{y_{1}}$

Eliminating c from (i) and (ii) , we get.

$y^{2} = \frac{2y}{y_{1}}\left( x + \frac{\sqrt{y}}{y_{1}} \right)$

⇒ $yy_{1} - 2x = 2\frac{\sqrt{y}}{y_{1}}$

⇒ $\left( yy_{1} - 2x \right)^{2}y_{1} = 4y$

Clearly, it is a differential equation of order one and degree 3.