求(y3一3xy2一3x2y)dx+(3xy2一3x2y—x3+y2)dy=0的通解.

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问题 求(y3一3xy2一3x2y)dx+(3xy2一3x2y—x3+y2)dy=0的通解.

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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 [*]

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