Question

If $y=a+b{x}^2;a,b$ are arbitrary constants then:

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

Answer 1

The correct option is B $x\frac{d^{2}y}{d{x}^2}=\frac{dy}{dx}$

$y=a+b{x}^2$

$y^{\prime }=2bx$

$\Rightarrow 2b=\frac{y^{\prime }}{x}$

$y^{\prime \prime }=2b=\frac{y^{\prime }}{x}$

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