解答题
11.求(y3一3xy2一3x2y)dx+(3xy2一3x2y—x3+y2)dy=0的通解．
【正确答案】将原给方程通过观察分项组合．
(y3一3xy2一3x2y)dx+(3xy2一3x2y—x3+y2)dy
=(y3dx+3xy2dy)一3xy(ydx+xdy)一(3x2ydx+x3dy)+y2dy
=0，
即
(y3一3xy2一3x2y)dx+(3xy2一3x2y—x3+y2)dy
=(y3dx+3xy2dy)一3xy(ydx+xdy)一(3x2ydx+x3dy)+y2dy
=0，
即
【答案解析】