What is expand y(x^3e^{xy}-y)dx+x(y+x^2e^{xy})dy ?

The solution to expand y(x^3e^{xy}-y)dx+x(y+x^2e^{xy})dy is e^{yx}yx^3dx-y^2dx+yxdy+e^{yx}x^3dy

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expand y(x^3e^{xy}-y)dx+x(y+x^2e^{xy})dy

expand

y (x^{3} e^{x y} - y) d x + x (y + x^{2} e^{x y}) d y

e^{y x} y x^{3} d x - y^{2} d x + y x d y + e^{y x} x^{3} d y

Solution steps

y (x^{3} e^{x y} - y) d x + x (y + x^{2} e^{x y}) d y

= y (e^{y x} x^{3} - y) d x + x (y + e^{y x} x^{2}) d y

Expand

y d x (x^{3} e^{x y} - y) : e^{y x} y x^{3} d x - y^{2} d x

= e^{y x} y x^{3} d x - y^{2} d x + x (y + x^{2} e^{x y}) d y

Expand

x d y (y + x^{2} e^{x y}) : y x d y + e^{y x} x^{3} d y

= e^{y x} y x^{3} d x - y^{2} d x + y x d y + e^{y x} x^{3} d y

(2 x^{2} - \frac{1}{2 x})^{12}

\frac{( x + 1 ) ^{2}}{4}

(x - y i)^{3}

lo g_{10} (x^{3} y^{- 10})

\frac{- 1 + 1 - 4 ( - π - 4 πn )}{2}

What is expand y(x^3e^{xy}-y)dx+x(y+x^2e^{xy})dy ?
The solution to expand y(x^3e^{xy}-y)dx+x(y+x^2e^{xy})dy is e^{yx}yx^3dx-y^2dx+yxdy+e^{yx}x^3dy