જો y = A nx + B nx, તો d^2 y d x^2 = - Vidyadip

MCQ

જો $y = A\cos nx + B\sin nx,$ તો ${{{d^2}y} \over {d{x^2}}} = $

A
${n^2}y$
B
$ - y$
✓
$ - {n^2}y$
D
એકપણ નહીં

✓

Answer

Correct option: C.

$ - {n^2}y$

c
(c) $y = A\cos (nx) + B\sin (nx)$

$\therefore dy/dx = - nA\sin (nx) + nB\cos (nx)$

Again $\frac{{{d^2}y}}{{d{x^2}}} = - {n^2}A\cos (nx) - {n^2}B\sin (nx)$

$ = - {n^2}[A\cos (nx) + B\sin (nx)]$

==> $\frac{{{d^2}y}}{{d{x^2}}} = - {n^2}y$.

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