Question

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

• A. order $3$
• B. order $2$
• C. degree $3$
• D. degree $4$

Answer 1

Answer: (C)

degree $3$

$y^2=2c(x+\sqrt{c})$
$\Rightarrow 2y{y}_1=2c$
$\Rightarrow c=y{y}_1$
$\Rightarrow y^2=2y{y}_1(x+\sqrt{y{y}_1})$
$\Rightarrow (\frac{y}{2y_1}-x{)}^2=y{y}_1$
$\Rightarrow (y-2x{y}_1{)}^2=4y{y}_1{}^3$
order $=1$
degree $=3$