Question

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

• A. $2,1$
• B. $1,2$
• C. $3,2$
• D. $2,3$

Answer 1

The correct option is B $1,2$

Equation of parabola is given by,

$(y-k{)}^2=a(x-h)$

differentiating on both sides, we get

$2(y-k)\frac{dy}{dx}=ax$

again differentiating on both sides, we get

$(y-k)\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2=\frac{a}{2}$

$\frac{ax}{2\frac{dy}{dx}}\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2=\frac{a}{2}$

$ax\frac{d^{2}y}{d{x}^2}+2{\left(\frac{dy}{dx}\right)}^3=a\frac{dy}{dx}$

$Order=2$

$Degree=1$