If d^2 y d x^2 + x = 0, then solution of the differential equatio… - Vidyadip

MCQ

If $\frac{{{d^2}y}}{{d{x^2}}} + \sin x = 0,$ then solution of the differential equation is.

✓
$\sin x + {c_1}x + {c_2}$
B
$\cos x + {c_1}x + {c_2}$
C
$\tan x + {c_1}x + {c_2}$
D
$\log \sin x + {c_1}x + {c_2}$

✓

Answer

Correct option: A.

$\sin x + {c_1}x + {c_2}$

a
(a) We have, $\frac{{{d^2}y}}{{d{x^2}}} + \sin x = 0$or $\frac{{{d^2}y}}{{d{x^2}}} = - \sin x$

On integrating, $\frac{{dy}}{{dx}} = - ( - \cos x) + {c_1}$ = $\cos x + {c_1}$

Again integrate, we get $y = \sin x + {c_1}x + {c_2}$.

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