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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