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Slove: (x+y)dx+(3x+3y-4)dy=0

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Solution:    Let   x+y=t   Rightarrow    1+fracmathrmd ymathrmd x=fracmathrmd tmathrmd x

                 Rightarrow     2 dx-3 dt +(2/2-t)dt=0

                Integrating and replacing    t  by   x+y , we get

                Rightarrow       2x-3t-2lnleft | 2-t ight |=c_1

              Rightarrow        2x-3(x+y)-2lnleft | (2-x-y) ight |=c_1

              Rightarrow      x+3y+2lnleft | (2-x-y) ight |=c

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Deependra Verma

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