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

The solution to expand (y-xy^2+2ye^x)dx+(x-x^2y+2e^x)dy is ydx-y^2xdx+2e^xydx+xdy-yx^2dy+2e^xdy

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expand (y-xy^2+2ye^x)dx+(x-x^2y+2e^x)dy

expand

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

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

Solution steps

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

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

Expand

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

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

Expand

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

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

(1 - i w)^{2}

a ln (\frac{am}{( a + b ) t}) + b ln (\frac{bm}{( a + b ) t})

\frac{( 8 ( a ^{2} - s ^{2} ) )}{( a ^{2} + s ^{2} ) ^{2}}

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

(5 + 6) (6 - 5)

What is expand (y-xy^2+2ye^x)dx+(x-x^2y+2e^x)dy ?
The solution to expand (y-xy^2+2ye^x)dx+(x-x^2y+2e^x)dy is ydx-y^2xdx+2e^xydx+xdy-yx^2dy+2e^xdy