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The general solution of the differential equation $\frac{d y}{d x}+\sin (x+y)=\sin (x-y)$ is
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Verified Answer
The correct answer is:
$\quad \log \tan \frac{y}{2}+2 \sin x=\mathrm{C}$
The equation is,
$\frac{d y}{d x}=\sin (x-y)-\sin (x+y)=2 \cos x \sin (-y)$
$\Rightarrow \frac{d y}{\sin y}+2 \cos x d x=0$
$\Rightarrow \int \cos e c y d y+2 \int \cos x d x=\mathrm{C}$
$\Rightarrow \log \tan \frac{y}{2}+2 \sin x=\mathrm{C}$
$\frac{d y}{d x}=\sin (x-y)-\sin (x+y)=2 \cos x \sin (-y)$
$\Rightarrow \frac{d y}{\sin y}+2 \cos x d x=0$
$\Rightarrow \int \cos e c y d y+2 \int \cos x d x=\mathrm{C}$
$\Rightarrow \log \tan \frac{y}{2}+2 \sin x=\mathrm{C}$
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