The order of the differential equation corresponding to the family of parabolas whose axes are along the…

1. 4
2. 3
3. 2
4. 1

Solution

The equation of family of parabolas with focus and the $x$-axis as axis is
Differentiating w.r.t. $x$, we get $ 2 y \frac{d y}{d x}=4 a \Rightarrow a=\frac{y}{2} \frac{d y}{d x} $ Substituting the value of $a$ in Eq. (i), we get $ \begin{aligned} & y^2=2 y \frac{d y}{d x}\left(x-\frac{y}{2}\right) \frac{d y}{d x} \\ \Rightarrow & y^2=y \frac{d y}{d x}\left(2 x-y \frac{d y}{d x}\right) \\ \Rightarrow & y\left(\frac{d y}{d x}\right)^2-2 x \frac{d y}{d x}+y=0 \end{aligned} $ It is clear from the differential equation is that the orders of equation is 1

Asked in: AP EAMCET 2019 (20 Apr Shift 2)

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