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