What is expand xy^4dx+(y^2+2)e^{-3x}dy ?

The solution to expand xy^4dx+(y^2+2)e^{-3x}dy is xy^4dx+e^{-3x}y^2dy+2e^{-3x}dy

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expand xy^4dx+(y^2+2)e^{-3x}dy

expand

x y^{4} d x + (y^{2} + 2) e^{- 3 x} d y

x y^{4} d x + e^{- 3 x} y^{2} d y + 2 e^{- 3 x} d y

Solution steps

x y^{4} d x + (y^{2} + 2) e^{- 3 x} d y

= x y^{4} d x + e^{- 3 x} (y^{2} + 2) d y

Expand

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

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

(t - \frac{1}{4}) (t - \frac{3}{4})

2 (x - 2) (x - 2) (x + 2)

(\frac{4}{16} x + \frac{5}{16} y + \frac{3}{16} z + \frac{4}{16} t)^{4}

(4 + 2 i)^{5}

e^{(1 + 2 i) t}

What is expand xy^4dx+(y^2+2)e^{-3x}dy ?
The solution to expand xy^4dx+(y^2+2)e^{-3x}dy is xy^4dx+e^{-3x}y^2dy+2e^{-3x}dy