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

MCQ

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

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

✓

Answer

Correct option: B.

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

b
(b)$\frac{{dy}}{{dx}} = 2bx,\;\;\frac{{{d^2}y}}{{d{x^2}}} = 2b$==> $x\frac{{{d^2}y}}{{d{x^2}}} = 2bx = \frac{{dy}}{{dx}}$.

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