erweitern (2xy^4e^y+2xy^3+y)dx+(x^2y^4e^y-x^2y^2-3x)dy

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

Multipliziere aus

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

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

Multipliziere aus

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

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

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

e x p an d A (5, - 2) B (- 1, 2)

e x p an d (2 c + d + e) (2 c + d - e)

e x p an d \frac{1}{( s - 2 ) ( s ^{2} + 1 )}

e x p an d \frac{( x - 8 ) ^{2}}{( x ^{2} - 16 )}