What is expand ((y+xy^3)dx+xdy=0)y+xy^3 ?

The solution to expand ((y+xy^3)dx+xdy=0)y+xy^3 is y^2dx+y^4xdx+yxdy=y^3x

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expand ((y+xy^3)dx+xdy=0)y+xy^3

expand

((y + x y^{3}) d x + x d y = 0) y + x y^{3}

y^{2} d x + y^{4} x d x + y x d y = y^{3} x

Solution steps

((y + x y^{3}) d x + x d y = 0) y + x y^{3}

= y ((y + y^{3} x) d x + 0 = x d y) + y^{3} x

Expand

y ((y + x y^{3}) d x + x d y = 0) : y^{2} d x + y^{4} x d x + y x d y = 0

y^{2} d x + y^{4} x d x + y x d y = 0 + x y^{3}

Expand

0 + x y^{3} : y^{3} x

y^{2} d x + y^{4} x d x + y x d y = y^{3} x

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What is expand ((y+xy^3)dx+xdy=0)y+xy^3 ?
The solution to expand ((y+xy^3)dx+xdy=0)y+xy^3 is y^2dx+y^4xdx+yxdy=y^3x