y = 4 3x is a solution of the differential equation - Vidyadip

MCQ

$y = 4\sin 3x$ is a solution of the differential equation

A
$\frac{{dy}}{{dx}} + 8y = 0$
B
$\frac{{dy}}{{dx}} - 8y = 0$
✓
$\frac{{{d^2}y}}{{d{x^2}}} + 9y = 0$
D
$\frac{{{d^2}y}}{{d{x^2}}} - 9y = 0$

✓

Answer

Correct option: C.

$\frac{{{d^2}y}}{{d{x^2}}} + 9y = 0$

c
(c) Let $y = 4\sin 3x \Rightarrow \frac{{dy}}{{dx}} = 12\cos 3x$

==> $\frac{{{d^2}y}}{{d{x^2}}} = - 36\sin 3x = - 9 \times 4\sin 3x = - 9y$

==> $\frac{{{d^2}y}}{{d{x^2}}} + 9y = 0$.

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