[e^(x+y)-e^x]dx+[e^(x+y)-e^y]dy=0求通解

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[e^(x+y)-e^x]dx+[e^(x+y)-e^y]dy=0求通解[e^(x+y)-e^x]dx+[e^(x+y)-e^y]dy=0求通解[e^(x+y)-e^x]dx+[e^(x+y)-e^y

[e^(x+y)-e^x]dx+[e^(x+y)-e^y]dy=0求通解
[e^(x+y)-e^x]dx+[e^(x+y)-e^y]dy=0求通解

[e^(x+y)-e^x]dx+[e^(x+y)-e^y]dy=0求通解
全微分方程
通解为(e^x-1)(e^y-1)+c

[e^(x+y) -e^x]dx +[e^(x+y) +e^y]dy=0

(e^y-1)de^x+(e^x+1)de^y=0

de^x/(e^x+1)  +de^y/(e^y-1)=0

dln(e^x+1)+dln(e^y-1)=0

ln(e^x+1)+ln(e^y-1)=C0

  (e^x+1)(e^y-1)=C