What is expand (2x+y)dx+(2ye^{y/x}-x)dy ?

The solution to expand (2x+y)dx+(2ye^{y/x}-x)dy is 2xdx+ydx+2e^{y/x}ydy-xdy

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expand (2x+y)dx+(2ye^{y/x}-x)dy

expand

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

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

Solution steps

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

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

Expand

d x (2 x + y) : 2 x d x + y d x

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

Expand

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

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

(x + i x^{2})^{2} - 2 (x + i x^{2}) (1 + 2 i x)

\frac{2 - e ^{- 3 π s}}{s ( s ^{2} + 1 )}

\frac{100 ( 0.02 x + 4 ) ^{3}}{x}

(f \circ g) (2 x - 1) (- x^{2})

\frac{s ^{2} ( s + 1 ) ( s + 30 ) ( s + 40 )}{( s + 2 ) ( s + 3 )}

What is expand (2x+y)dx+(2ye^{y/x}-x)dy ?
The solution to expand (2x+y)dx+(2ye^{y/x}-x)dy is 2xdx+ydx+2e^{y/x}ydy-xdy