The differential equation of all parabolas wh | vedclass

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Question

(A) The general equation of a parabola with its axis parallel to the $y$-axis is given by $y = Ax^2 + Bx + C$,where $A, B, C$ are arbitrary constants.

Vedclass · Accepted Answer

$\frac{d^3y}{dx^3} = 0$

Vedclass · Answer

(A) The general equation of a parabola with its axis parallel to the $y$-axis is given by $y = Ax^2 + Bx + C$,where $A, B, C$ are arbitrary constants.Step $1$: Differentiate with respect to $x$:$\frac{dy}{dx} = 2Ax + B$Step $2$: Differentiate again with respect to $x$:$\frac{d^2y}{dx^2} = 2A$Step $3$: Differentiate a third time with respect to $x$:$\frac{d^3y}{dx^3} = 0$Since there are $3$ arbitrary constants,we differentiate $3$ times to eliminate them. Thus,the required differential equation is $\frac{d^3y}{dx^3} = 0$.

The differential equation of all parabolas whose axes are parallel to the $y$-axis is

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