If d^2 y d x^2 = 0, then - Vidyadip

MCQ

If $\frac{{{d^2}y}}{{d{x^2}}} = 0,$ then

✓
$y = ax + b$
B
${y^2} = ax + b$
C
$y = \log x$
D
$y = {e^x} + c$

✓

Answer

Correct option: A.

$y = ax + b$

a
(a) $\frac{{{d^2}y}}{{d{x^2}}} = 0$ ==> $\frac{d}{{dx}}\left( {\frac{{dy}}{{dx}}} \right) = 0$.....$(i)$

Integrating $(i)$ with respect to $x$, $\frac{{dy}}{{dx}} = a$…..$(ii)$

where $a$ is an arbitrary constant

Again integrating $(ii)$ with respect to $x$

$\int {\frac{{dy}}{{dx}}dx} = \int {adx + b} $ or $y = ax + b$,

where $b$ is another arbitrary constant.

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