The degree and order of the differential equa | vedclass

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(B) The general equation of a parabola with its axis as the $x$-axis is given by $y^2 = 4a(x - h)$,where $a$ and $h$ are arbitrary constants.Since the

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$1, 2$

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(B) The general equation of a parabola with its axis as the $x$-axis is given by $y^2 = 4a(x - h)$,where $a$ and $h$ are arbitrary constants.Since there are two arbitrary constants,we differentiate the equation twice.First derivative: $2y y_1 = 4a$,which simplifies to $y y_1 = 2a$.Second derivative: $y_1^2 + y y_2 = 0$.In the differential equation $y_2 y + y_1^2 = 0$,the highest order derivative is $y_2$,so the order is $2$.The power of the highest order derivative $y_2$ is $1$,so the degree is $1$.Therefore,the degree is $1$ and the order is $2$.

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

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