Question

The differential equation of all parabolas each of which has a latus rectum ' $4 a ^{\prime} \&$ whose axes are parallel to $x$-axis is :

• A. of order $1 \&$ degree 2
• B. of order $2 \&$ degree 3
• C. of order 2 and degree 1
• D. of order 2 and degree 2

Answer 1

Answer: (C)

Equation to the family of parabolas is $(y-k)^2=4 a(x-h)$
$2(y-k) \frac{d y}{d x}=4 a \Rightarrow (y-k) \frac{d y}{d x}=2 a $
$(y-k) \frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2=0$
$2 a \frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^3=0$.
Hence order is 2 and degree is 1 .