erweitern (xy-1)^2((xy^2-y)dx+(x^2y+x)dy=0)

Lösung

erweitern

(x y - 1)^{2} ((x y^{2} - y) d x + (x^{2} y + x) d y = 0)

x^{3} y^{4} d x - 3 x^{2} y^{3} d x + 3 x y^{2} d x - y d x + x^{4} y^{3} d y - x^{3} y^{2} d y - x^{2} y d y + x d y = 0

Schritte zur Lösung

(x y - 1)^{2} ((x y^{2} - y) d x + (x^{2} y + x) d y = 0)

= (x y - 1)^{2} ((x y^{2} - y) d x + 0 = (x^{2} y + x) d y)

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = (x y - 1)^{2}, b = (x y^{2} - y) d x, c = (x^{2} y + x) d y = 0

(x y - 1)^{2} (x y^{2} - y) d x + (x y - 1)^{2} (x^{2} y + x) d y = 0

Multipliziere aus

(x y - 1)^{2} (x y^{2} - y) d x + (x y - 1)^{2} (x^{2} y + x) d y : x^{3} y^{4} d x - 3 x^{2} y^{3} d x + 3 x y^{2} d x - y d x + x^{4} y^{3} d y - x^{3} y^{2} d y - x^{2} y d y + x d y

x^{3} y^{4} d x - 3 x^{2} y^{3} d x + 3 x y^{2} d x - y d x + x^{4} y^{3} d y - x^{3} y^{2} d y - x^{2} y d y + x d y = 0

e x p an d \frac{r \cdot ( 4 r ^{2} sin ^{2} ( θ ) - r ^{4} )}{2}

e x p an d 5 (7 - x = 31 - x)

e x p an d (1 - \frac{4}{x}) e^{x}

e x p an d \frac{11 ( 3 11 + 3 3 - 3 - 33 )}{12}

e x p an d \frac{( ( s cos ( θ ) ) - w ( sin ( θ ) ) )}{( s + a ) ( s ^{2} + w ^{2} )}