The solution of the differential equation. yex/ydx=(xex/y+y2siny)dy is.
A
ex/y=−cosy+c
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B
ey/x=−cosy+c
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C
ex/y=cosy−c
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D
ey/x=cosy+c
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Solution
The correct option is Aex/y=−cosy+c Given, yex/ydx=(xex/y+y2siny)dy ⇒(ydx−xdy)ex/y=y2sinydy ⇒ex/y(ydx−xdyy2)=sinydy ⇒ex/yd(xy)=−d(cosy) On integrating, we get ex/y=−cosy+c