If y = a e^ mx + b e^ - mx , then d^2 y d x^2 - m^2 y = - Vidyadip

MCQ

If $y = a{e^{mx}} + b{e^{ - mx}}$, then ${{{d^2}y} \over {d{x^2}}} - {m^2}y = $

A
${{m}^{2}}(a{{e}^{mx}}-b{{e}^{-mx}})$
B
$1$
✓
$0$
D
None of these

✓

Answer

Correct option: C.

$0$

c
(c) $y = a{e^{mx}} + b{e^{ - mx}};$

$\therefore \frac{{dy}}{{dx}} = am{e^{mx}} - mb{e^{ - mx}}$

Again $\frac{{{d^2}y}}{{d{x^2}}} = a{m^2}{e^{mx}} + {m^2}b{e^{ - mx}}$

==> $\frac{{{d^2}y}}{{d{x^2}}} = {m^2}(a{e^{mx}} + b{e^{ - mx}}) \Rightarrow \frac{{{d^2}y}}{{d{x^2}}} = {m^2}y$

or $\frac{{{d^2}y}}{{d{x^2}}} - {m^2}y = 0$.

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