Question

The differential equation to the family of parabola having latus rectum $4a$ and axis parallel to the $x-$axis is

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

Answer 1

The correct option is C of order $2$ and degree $1$

Equation to the family of parabolas is $(y-k{)}^2=4a(x-h),$ (where $h,k$ are constants)
$\Rightarrow (y-k)\frac{dy}{dx}=2a\cdots \left(i\right)$
$\Rightarrow (y-k)\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2=0$
$\Rightarrow 2a\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^3=0\left(\text{substituting}\right(y-k\left)\text{from equation}\right(i\left)\right)$
Hence the order is $2$ and the degree is $1$