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Question

Solution of the differential equation xdx+ydyxdxydy=y3x3 is given by

A
32log(yx)+log∣ ∣x32+y32x32∣ ∣+tan1(yx)32+c=0
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B
23log(yx)+log∣ ∣x32+y32x32∣ ∣+tan1yx+c=0
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C
23log(yx)+log(x+yx)+tan1(y32x32)+c=0
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D

None of the above

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Solution

The correct option is D

None of the above


we have xdx+ydyxdxydy=y3x3
d(x32)+d(y32)d(x32)d(y32)=y32x32du+dvdudv=vu,whereu=x32andv=y32udu+udv=vduvduudu+vdv=vduudvudu+vdvu2+v2=vduudvu2+v2d(u2+v2)u2+v2=2dtan1(vu)
On integrating, we get
log(u2+v2)=2tan1(vu)+c12log(x3+y3)+tan1(yx)32=c

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