erweitern (1+2e^{x/y})dx+2e^{x/y}(1-x/y)dy

Lösung

erweitern

(1 + 2 e^{\frac{x}{y}}) d x + 2 e^{\frac{x}{y}} (1 - \frac{x}{y}) d y

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

Schritte zur Lösung

(1 + 2 e^{\frac{x}{y}}) d x + 2 e^{\frac{x}{y}} (1 - \frac{x}{y}) d y

Multipliziere aus

d x (1 + 2 e^{\frac{x}{y}}) : d x + 2 e^{\frac{x}{y}} d x

= d x + 2 e^{\frac{x}{y}} d x + 2 e^{\frac{x}{y}} (1 - \frac{x}{y}) d y

Multipliziere aus

2 e^{\frac{x}{y}} d y (1 - \frac{x}{y}) : 2 e^{\frac{x}{y}} d y - \frac{2 e ^{\frac{x}{y}} x d y}{y}

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

e x p an d e^{x} (x^{2} + x)

e x p an d n (\frac{( 4 - π ) θ}{4 n} + \frac{π θ}{4})

e x p an d \frac{d}{d x} ((x - 1) (x - 6)^{3}) + 9

e x p an d e^{x} (x^{2} - 1)

e x p an d y sin (x) + x y cos (x) d x + (x sin (x) + 1) d y