Solution of the differential equation dy dx y = (x + y) + (x - y)… - Vidyadip

MCQ

Solution of the differential equation $\frac{{dy}}{{dx}}\tan y = \sin (x + y) + \sin (x - y)$ is

✓
$\sec y + 2\cos x = c$
B
$\sec y - 2\cos x = c$
C
$\cos y - 2\sin x = c$
D
$\tan y - 2\sec y = c$

✓

Answer

Correct option: A.

$\sec y + 2\cos x = c$

a
(a) $\frac{{dy}}{{dx}}\tan y = \sin (x + y) + \sin (x - y)$

$\frac{{dy}}{{dx}}(\tan y) = 2\sin x\cos y$ ==> $\frac{{\sin y}}{{{{\cos }^2}y}}dy = 2\sin xdx$

==> $\int {\frac{{\sin y}}{{{{\cos }^2}y}}} dy = 2\int {\sin xdx} $ ==> $\frac{1}{{\cos y}} = - 2\cos x + c$

$\therefore$ $\sec y + 2\cos x = c$.

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