Question

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

• A. $\frac{d^{3}y}{{dx}^3}=0$
• B. $\frac{d^{2}y}{{dx}^2}$
• C. $\frac{d^{2}y}{{dx}^2}+\frac{dy}{dx}=0$
• D. $\frac{d^{2}y}{{dx}^2}+\frac{dy}{dx}+y=0$

Answer 1

The correct option is A $\frac{d^{3}y}{{dx}^3}=0$

The equation of a member of the family of parabolas having axis parallel to y-axis is $y={Ax}^2+Bx+C$, where A, B, and C are arbitrary constants.

$\Rightarrow \frac{dy}{dx}=2Ax+B$

$\Rightarrow \frac{d^{2}y}{{dx}^2}=2A$

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