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Question

The solution of the differential equation dydx+3x21+x3 y=sin2 x1+x3 is


A

y(1+x3)=x+12 sin 2x+c

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B

2 tan1(xy)+log x+c=0

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C

log(y+x2+y2)+log y+c=0

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D

sin h1(xy)+log y+c=0

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Solution

The correct option is D

sin h1(xy)+log y+c=0


dydx+3x21+x3 y=sin2 x1+x3P=3x21+x3I.F.=e p dx=elog(1+x3)=1+x3
Thus the solution is
y.(1+x3)=sin2 x1+x3(1+x3) dx=1cos 2x2 dxy(1+x3)=12 xsin 2x4+c.


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