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Question

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


A

y=12x2+x+c

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B

logy+1=12x2+x+c

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C

cy+1=ex2+x

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D

None of these.

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Solution

The correct option is B

logy+1=12x2+x+c


Explanation of the correct option.

Compute the required value.

Given : dydx=xy+x+y+1

dydx=x(y+1)+y+1

dydx=(x+1)(y+1)

dyy+1=(x+1)dx

Now, Integrate both side,

logy+1=x22+x+c 1x+adx=logx+a,xndx=xn+1

Hence option B is the correct option.


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