erweitern (xy^2-kx^2y)dx+(x-y)x^2dy

Lösung

erweitern

(x y^{2} - k x^{2} y) d x + (x - y) x^{2} d y

x y^{2} d x - k x^{2} y d x + x^{3} d y - x^{2} y d y

Schritte zur Lösung

(x y^{2} - k x^{2} y) d x + (x - y) x^{2} d y

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

Multipliziere aus

d x (x y^{2} - k x^{2} y) : x y^{2} d x - k x^{2} y d x

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

Multipliziere aus

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

= x y^{2} d x - k x^{2} y d x + x^{3} d y - x^{2} y d y

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

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

e x p an d (6 x + 9 y + 11) d x + (9 x - 4 y + 3) d y

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

s im pl i f y cos (x) (cos (x) + (- s) in x)