Question

Form the differential equation from the following primitive, where constant is arbitrary.

$y=a{x}^2+bx+c$

• A. $\frac{dy}{dx}=0$
• B. $\frac{d^{2}y}{d{x}^2}=0$
• C. $\frac{d^{3}y}{d{x}^3}=0$
• D. None of these

Answer 1

The correct option is C $\frac{d^{3}y}{d{x}^3}=0$

$y=a{x}^2+bx+c$

$⟹\frac{dy}{dx}$$=\frac{d}{dx}(a{x}^2+bx+c)$

$\frac{dy}{dx}=2ax+b$

$⟹\frac{d^{2}y}{d{x}^2}=\frac{d}{dx}(2ax+b)=2a$

$\frac{d^{3}y}{d{x}^3}=\frac{d}{dx}\left(2a\right)$

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