第2308题：解微分方程
计算以下微分方程的通解.
(ex+y+ex)dx(\mathrm{e}^{x+y}+\mathrm{e}^x)dx(ex+y+ex)dx +(ex+y−ey)dy=0+(\mathrm{e}^{x+y}-\mathrm{e}^y)dy=0+(ex+y−ey)dy=0
A. y+x=Cy+x=Cy+x=C
B. exey=C\mathrm{e}^x \mathrm{e}^y=Cexey=C
C. (ex−1)(ey+1)=C (\mathrm{e}^{x}-1)(\mathrm{e}^y+1)=C(ex−1)(ey+1)=C
D. (ex+1)(ey−1)=C(\mathrm{e}^{x}+1)(\mathrm{e}^y-1)=C(ex+1)(ey−1)=C
注：
∫dxax+b\int \dfrac{dx}{ax+b}∫ax+bdx =1aln∣ax+b∣+C=\dfrac{1}{a} \ln | ax+b | + C=a1ln∣ax+b∣+C
