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

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

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.To find the differential equation,we differentiate with respect to $x$ three times to eliminate the three constants.First derivative: $\frac{dy}{dx} = 2Ax + B$.Second derivative: $\frac{d^2y}{dx^2} = 2A$.Third derivative: $\frac{d^3y}{dx^3} = 0$.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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