已知df(x,y)=(2y^2+2xy+3x^2)dx+(4xy+x^2)dy,求f(x,y)答案是2xy^2+x^2y+x^3+C

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已知df(x,y)=(2y^2+2xy+3x^2)dx+(4xy+x^2)dy,求f(x,y)答案是2xy^2+x^2y+x^3+C
已知df(x,y)=(2y^2+2xy+3x^2)dx+(4xy+x^2)dy,求f(x,y)
答案是2xy^2+x^2y+x^3+C

已知df(x,y)=(2y^2+2xy+3x^2)dx+(4xy+x^2)dy,求f(x,y)答案是2xy^2+x^2y+x^3+C
对y的偏导就是4xy+x^2,对y积分得到2xy^2+x^2y+g(x)
对x的偏导就是2y^2+2xy+3x^2,对x积分得到2xy^2+x^2y+x^3+h(y)
综合得到2xy^2+x^2y+x^3+C

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