Question

The order of differential equation of all the parabolas whose axis is along positive $x$ axis and vertex is at origin is

• A. $2$
• B. $1$
• C. $3$
• D. not defined

Answer 1

The correct option is B $1$

Let the equation of the parabola be $y^2=4ax$
Differentiating w.r.t. x
$2y{y}^{\prime }=4a........\left(1\right)$
substituting equation $\left(1\right)$ in the given parabola,
$y^2=2y{y}^{\prime }x\Rightarrow y=2x{y}^{\prime }\Rightarrow y^{\prime }-\frac{y}{2x}=0$
Hence, the order of the D.E is $1$