Question

# Solution of the differential equation: x+ydydxyâˆ’xdydx=xsin2(x2+y2)y3

A
cot(x2+y2)=(xy)2+c
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B
y2x2+y2c=tan2(x2+y2)
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C
cot(x2+y2)=(yx)2+c
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D
y2+x2cx2=tan2(x2+y2)
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Solution

## The correct options are A −cot(x2+y2)=(xy)2+c B y2x2+y2c=−tan2(x2+y2)The given differential equation can be written as xdx+ydyydx−xdy=xsin2(x2+y2)y3⇒2xdx+2ydyydx−xdy=2xsin2(x2+y2)y3⇒d(x2+y2)sin2(x2y2)=2xy3(ydx−xdy)⇒cosec2(x2+y2)d(x2+y2)=2(xy)d(xy) On integrating, we get ∫cosce2(x2+y2)d(x2+y2)=2∫(xy)d(xy) −cot(x2+y2)=(xy)2+c y2x2+y2c=−tan2(x2+y2)

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