求全微分方程sin(x+y)dx+[xcos(x+y)](dx+dy)=0的通解.答案为xsin求全微分方程sin(x+y)dx+[xcos(x+y)](dx+dy)=0的通解.答案为xsin(x+y)=C.

Question

求全微分方程sin(x+y)dx+[xcos(x+y)](dx+dy)=0的通解.答案为xsin
求全微分方程sin(x+y)dx+[xcos(x+y)](dx+dy)=0的通解.
答案为xsin(x+y)=C.

Answer 1

设x+y=u,u'=1+y'
原方程即sin(x+y)+[xcos(x+y)](1+dy/dx)=0
即sinu+xcosu*u'=0
u'=-tanu/x
du/tanu=-dx/x
ln|sinu|=-ln|x|+C0
sinu=C/x
即xsin(x+y)=C