The solution of the differential equation,  dydx=(x−y)2, when y(1)=1 is 

The solution of the differential equation,  dydx=(xy)2, when y(1)=1 is 

  1. A

    loge1+xy1x+y=x+y2

  2. B

    loge2x2y=xy

  3. C

    logc1x+y1+xy=2(x1)

  4. D

    logc2y2x=2(y1)

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    Solution:

    Given, dydx=(xy)2 

    Let, xy=tdydx=1dtdx  1dtdx=t2

    dt1t2=dx12loge1+t1t=x+c12loge1+xy1x+y=x+C

    Given, y(1)=1

    12loge(1)=C+1C=1 loge1+xy1x+y=2(x1)loge1x+y1+xy=2(x1)

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