The general solution of dydx= x + sinx cosy + x cosy + sinx is

dydx=(x+sinx) (1+ cosy)∫dy1+cosy=∫(x+sinx) dx∫12sec2 (y/2) dy =∫(x + sin x) dx⇒ tan (y2) = x22-cos x + c

The general solution of dydx= x + sinx cosy + x cosy + sinx is

dydx=(x+sinx) (1+ cosy)∫dy1+cosy=∫(x+sinx) dx∫12sec2 (y/2) dy =∫(x + sin x) dx⇒ tan (y2) = x22-cos x + c

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The general solution of $\frac{d y}{d x} = x + sinx cosy + x cosy + sinx$ is

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${Sec}^{2} (\frac{y}{2}) = \frac{x^{2}}{2} -cosx + c$

$Tan (\frac{y}{2}) = \frac{x^{2}}{2} -cosx + c$

$Tan (\frac{y}{2}) = \frac{x^{2}}{2} + cosx + c$

$Tan (\frac{x}{2}) = \frac{y^{2}}{2} -cosy + c$

answer is B.

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Detailed Solution

$\frac{dy}{dx} = (x+sinx) (1+ cosy)$

$\int \frac{dy}{1+cosy} = \int (x+sinx) dx$

$\int \frac{1}{2} {sec}^{2} (y/2) dy = \int (x + sin x) dx$

$\Rightarrow tan (\frac{y}{2}) = \frac{x^{2}}{2} -cos x + c$

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The general solution of dydx= x + sinx cosy + x cosy + sinx is

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The general solution of $\frac{d y}{d x} = x + sinx cosy + x cosy + sinx$ is