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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

Multipliziere aus

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

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

Multipliziere aus

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

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

e x p an d lo g_{10} (4) x^{2}

s im pl i f y (5 - x + 1)^{2}

e x p an d (1 - cos (4 x))^{2} + ln^{2} (1 + 3 x^{2}) - sin^{5} (4 x)

e x p an d (2 n - \frac{1}{2})^{3}

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