If y=a+bx^2,a,b arbitrary constants, then - Vidyadip

MCQ

If $\text{y}=\text{a}+\text{bx}^2,\text{a,b}$ arbitrary constants, then

A
$\frac{\text{d}^2\text{y}}{\text{dx}^2}=2\text{xy}$
✓
$\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}=\text{y}_1$
C
$\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}-\frac{\text{dy}}{\text{dx}}+\text{y}=0$
D
$\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}=2\text{xy}$

✓

Answer

Correct option: B.

$\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}=\text{y}_1$

$\text{y}=\text{a}+\text{bx}^2$
$\Rightarrow\text{y}_1=2\text{bx}$
$\Rightarrow\text{y}_2=2\text{b}$
Multiply by x on both sides we get
$\text{xy}_2=2\text{bx}=\text{y}_1$
$\Rightarrow\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}=\text{y}_1$

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