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

The solution to expand ((y+2x)dy+dx)e^{2y} is e^{2y}ydy+2e^{2y}xdy+e^{2y}dx

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

expand

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

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

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

a = e^{2 y}, b = (y + 2 x) d y, c = d x

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

Expand

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

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

\frac{d ^{2}}{d x ^{2}} ((y) (2 x^{3} - 3 y^{2}))

(x - 4) (x - 2 + 7)

\frac{e ^{- 0.5 x} ( x + 1 )}{x ( x + 2 ) ( x + 3 )}

\frac{3 ( 3 3 - π )}{27 - π ^{2}}

(x^{5} - 2 x^{2} + 1) l e f t (x^{3} - x^{2} + 1)

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