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Solve : $ y dx +x dy +\sin y \cos ^2 (xy) dy+e^x \cos^2 (xy) dx=0$

$(a)\;\tan xy -\cos y=c \\ (b)\;\tan xy+e^x-\cos y=c \\ (c)\;e^x-\tan xy=c \\ (d)\;\sec xy-e^x- \sin y =c $
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divide by $\cos^2 (xy)$
$\large\frac{y dx+x dy}{\cos^2 (xy)}$$+\sin y dy +e^x dx=0$
$\large\frac{d(xy)}{\cos^2 (xy)}$$+\sin y dy +e^x dx=0$
$\sec^2 (xy) d(xy) +e^x dx+ \sin y dy=0$
Integrate:
$\tan xy +e^x - \cos y =c$
Hence b is the correct answer.
answered Feb 6, 2014 by meena.p
 

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