The degree and order of the differential equa | vedclass

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(C) The equation of the family of parabolas with the $X$-axis as their axis is given by $y^2 = 4a(x - b)$, where $a$ and $b$ are arbitrary constants.T

Vedclass · Accepted Answer

$1$, $2$

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(C) The equation of the family of parabolas with the $X$-axis as their axis is given by $y^2 = 4a(x - b)$, where $a$ and $b$ are arbitrary constants.To eliminate these two constants, we differentiate with respect to $x$:$2y \frac{dy}{dx} = 4a \implies y \frac{dy}{dx} = 2a$.Differentiating again with respect to $x$:$y \frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 = 0$.The highest order derivative present is $\frac{d^2y}{dx^2}$, so the order is $2$.The power of the highest order derivative is $1$, so the degree is $1$.Thus, the degree and order are $1$ and $2$ respectively.

The degree and order of the differential equation of the family of parabolas whose axis is the $X$-axis, are respectively

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