Question

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

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

Answer 1

The correct option is C degree $3$

$y\frac{dy}{dx}=2d\Rightarrow d=\frac{ydy}{dx}$
$y^2=2y\frac{dy}{dx}(x+\sqrt{y\frac{dy}{dx}})$
$y^2=2y\frac{dy}{dx}+2y^{3/2}{\left(\frac{dy}{dx}\right)}^{3/2}$
${(y^2-2y\frac{dy}{dx})}^2=4y^3{\left(\frac{dy}{dx}\right)}^3$
degree is $three$