The solution of the differential equation ydx−xdy=y2tan(xy)dx is
( C is constant of integration)
A
xy=Cex
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B
sin(xy)=Cex
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C
cos(xy)=Cex
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D
x=Cy
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Solution
The correct option is Bsin(xy)=Cex ydx−xdy=y2tan(xy)dx ⇒cotxy(ydx−xdyy2)=dx ⇒cot(xy)d(xy)=dx
Integrating both sides, we get log(sinxy)=x+logC ⇒sinxy=ex+logC=Cex