First slide

Formation of differential equations

Question

The differential equation of all parabolas whose axes are parallel to the axis of ‘y’ is

Easy

A

$\frac{d^{3} y}{{dx}^{3}} = 1$
B

$\frac{d^{3} y}{{dx}^{3}} = - 1$
C

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

$\frac{d^{3} y}{{dx}^{3}} = 2$

Solution

$The equation of the parabola is y = {ax}^{2} + bx + c$
$\begin{array}{l} \frac{d y}{d x} = 2 a x + b \\ \frac{d^{2} y}{d x^{2}} = 2 a \\ \frac{d^{3} y}{d x^{3}} = 0 \end{array}$

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