求解dy/dx=(x+y)/(x+y+1)解到1/2*(x+y+1)+1/4*In|2x+2y+1|=x+C就不知道怎么继续了.

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求解dy/dx=(x+y)/(x+y+1)解到1/2*(x+y+1)+1/4*In|2x+2y+1|=x+C就不知道怎么继续了.求解dy/dx=(x+y)/(x+y+1)解到1/2*(x+y+1)+1

求解dy/dx=(x+y)/(x+y+1)解到1/2*(x+y+1)+1/4*In|2x+2y+1|=x+C就不知道怎么继续了.
求解dy/dx=(x+y)/(x+y+1)
解到1/2*(x+y+1)+1/4*In|2x+2y+1|=x+C就不知道怎么继续了.

求解dy/dx=(x+y)/(x+y+1)解到1/2*(x+y+1)+1/4*In|2x+2y+1|=x+C就不知道怎么继续了.
x+y+1=u 求导得:1+y'=u'
代入dy/dx=(x+y)/(x+y+1)
u'-1=1-1/u
u'=2-1/u=(2u-1)/u
udu/(2u-1)=dx
2udu/(2u-1)=2dx
(2u-1+1)du/(2u-1)=2dx 积分得:
u+(1/2)ln(2u-1)=2x+lnC/2
ln(2u-1)=4x-2u+lnC
2u-1=Ce^(4x-2u)
或:2x+2y+1=Ce^(2x-2y-1)