The differential equation whose solution is y = A x + B x, is - Vidyadip

MCQ

The differential equation whose solution is $y = A\sin x + B\cos x,$ is

✓
$\frac{{{d^2}y}}{{d{x^2}}} + y = 0$
B
$\frac{{{d^2}y}}{{d{x^2}}} - y = 0$
C
$\frac{{dy}}{{dx}} + y = 0$
D
None of these

✓

Answer

Correct option: A.

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

a
(a) $y = A\sin x + B\cos x$==> $\frac{{dy}}{{dx}} = A\cos x - B\sin x$

==> $\frac{{{d^2}y}}{{d{x^2}}} = - A\sin x - B\cos x$$ = - (A\sin x + B\cos x) = - y$

==> $\frac{{{d^2}y}}{{d{x^2}}} + y = 0$ is the required differential equation.

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