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Q.

The solution of the differential equation dydx=xy+x+y+1 is

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a

y=12x2+x+C

b

log(y+1)=12x2+x+C

c

C(y+1)=ex2+2x2

d

y=12x3+x+C

answer is B.

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Detailed Solution

dydx=xy+x+y+1=xy+1+y+1=x+1y+1⇒dyy+1=x+1dxIntegration on both sides⇒∫dyy+1=∫dxlogy+1=x22+x+C
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