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Find the general solution of each of the following differentia

Question

Find the general solution of each of the following differential equations:
$\frac{d y}{d x} + sin (x + y) = sin (x - y)$ .

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Find the general solution of each of the following differential equations:

\frac{d y}{d x} + sin (x + y) = sin (x - y)

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Text solutionVerified

Given,

\frac{d y}{d x} + sin (x + y) = sin (x - y)

\Rightarrow \frac{d y}{d x} = sin (x - y) - sin (x + y)

\Rightarrow \frac{d y}{d x} = 2 cos (\frac{x - y + x + y}{2}) sin (\frac{x - y - x - y}{2}) [sin C - sin D = 2 cos (\frac{C + D}{2}) sin (\frac{C - D}{2})]

\Rightarrow \frac{d y}{d x} = 2 cos (\frac{x + x}{2}) sin (\frac{- y - y}{2})

\Rightarrow \frac{d y}{d x} = 2 cos (x) sin (- y)

\Rightarrow \frac{d y}{d x} = - 2 cos (x) sin (y)

\Rightarrow \frac{d y}{sin x} = - 2 cos x d x

int e g r a t in g b o t h s i d es

\int \frac{d y}{sin x} = - 2 \int cos x d x

\Rightarrow ln sin (\frac{x}{2}) = - 2 sin x + c

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Question Text	Find the general solution of each of the following differential equations: $\frac{d y}{d x} + sin (x + y) = sin (x - y)$ .
Answer Type	Text solution:1
Upvotes	150